How to answer graphing questions

Watch the how-to graphing videos

Number lines shows open and closed dots, segments and rays, and how to fix a drawing. Coordinate grids shows points, lines, inequalities and parabolas, plus keyboard entry at 3:32. Read either transcript for the same steps.

Graphing Your Answers

Some questions ask you to answer by drawing on a number line or a coordinate grid. These two videos show the graphing tool step by step. Both videos have captions. You can turn them on or off in the player.

Do you use a keyboard or a screen reader? You can type your graph instead of drawing it. The Coordinate grids video shows how at 3:32, and its transcript has the same steps.

Number lines 3 min 6 s

Read the transcript

0:00 How to graph your answers: number lines

Some homework questions ask you to answer by drawing on a number line. Every example in this video uses the same graphing tool as your homework.

0:10 The graphing toolbar

Every graphing question has a graph and a row of tools under it. Pick a tool first, then click the graph. Number line questions use up to three tools: the Line segments and rays tool, the Closed dot tool, and the Open dot tool. Everything you draw stays on the line. Most graphs move each click to the nearest grid mark, so you don't need to click exactly on a mark. Clear All erases everything you drew on that graph. There is no undo. Whenever you need to redraw a graph, click Clear All. It clears only the graph it sits under: a question with two graphs has two Clear All buttons.

0:50 Example 1 · An inequality: one dot and a ray

Graph x is greater than or equal to negative two on the number line. Choose the Closed dot tool. The symbol greater than or equal to includes negative two, so its dot is filled in. Click negative two on the number line. Now choose the Line segments and rays tool. Click negative two to start the ray. Click the last number at the right end of the line, ten. An arrowhead appears, so the graph keeps going to the right.

1:20 Example 2 · An interval: two dots and a segment

Graph the interval from negative three to four, with a parenthesis at negative three and a square bracket at four, on the number line. Choose Open dot. The parenthesis leaves negative three out, so its dot is open. Click negative three on the number line. Choose Closed dot. The square bracket includes four. Click four on the number line. Choose Line segments and rays, then click negative three and four to join the dots.

1:51 Example 3 · Two pieces: rays going opposite ways

Graph x is less than negative one or x is greater than or equal to two on the number line. Choose Open dot and click negative one. The symbol less than leaves negative one out. Choose Closed dot and click two. The symbol greater than or equal to includes two. Choose Line segments and rays. Click negative one, then the first number at the left end, negative ten, to draw a ray going left. Click two, then the last number at the right end, ten, to draw the second ray.

2:27 Redraw with Clear All

The segment and its dots are separate pieces. If you move the end of a segment, move its dot too. There is no undo. If you need to redraw a graph, click Clear All and draw it again. Your drawing is your answer. Submit the question the same way you submit any other answer. To practice, use the interactive graphing guide. On each example, press the Watch the steps button to see it done. Then press Try it yourself. Do you use a keyboard or a screen reader? You can type your graph instead. The coordinate grids video and the graphing guide have the steps.

Coordinate grids 4 min 29 s

Read the transcript

0:00 How to graph your answers: coordinate grids

Some homework questions ask you to answer by drawing on a coordinate grid. Every example in this video uses the same graphing tool as your homework. Pick a tool first, then click the graph. Each tool draws one kind of shape from the points you click. Coordinate grid tools show only a picture, not a name. Watch which picture the pointer clicks in each example. A shape is finished only after its last click. Clicking outside the graph, even on a button, erases a shape you haven't finished. Most graphs move each click to the nearest grid mark, so you don't need to click exactly on a line. Clear All erases everything you drew on that graph. There is no undo. Whenever you need to redraw a graph, click Clear All. It clears only the graph it sits under: a question with two graphs has two Clear All buttons.

0:53 Example 4 · Plot points

Plot the points two comma three, negative four comma one, and zero comma negative five. This question opens with the Line tool selected. Choose the Dot tool first. Click two comma three: from the origin, two right and three up. Click negative four comma one: four left and one up. Click zero comma negative five. It sits on the y axis.

1:21 Example 5 · Graph a line from two points

Graph y equals two x minus three. Find two points on the line. When x equals zero, y equals negative three. When x equals two, y equals two times two minus three equals one. With the Line tool selected, click zero comma negative three. Move to two comma one and click. The line runs through both points to the edges of the graph.

1:47 Example 6 · Graph a linear inequality

Graph y is less than two x plus one. The symbol less than leaves out the boundary, so choose Linear inequality, dashed line. Solid is for less than or equal to, or greater than or equal to. Click two points on the boundary line, y equals two x plus one. Click zero comma one, then one comma three. Move the pointer. The shading follows it. To pick a side, test the point two comma zero. Put x equals two and y equals zero into the inequality. Zero is less than two times two plus one, which is true, so click two comma zero to shade that side. The inequality is finished only after this third click.

2:33 Example 7 · Graph a parabola: vertex first

Graph f of x equals the quantity x minus one, squared, minus four. Choose the Parabola tool. A parabola needs its vertex and one more point. Click the vertex first. For this function, the vertex is one comma negative four. Click one more point on the parabola. f of three equals zero, so click three comma zero. The tool draws the whole parabola.

3:00 Example 8 · Move a point, then remove one

Plot the point two comma three. This graph already has two mistakes on it. The dot at three comma two belongs at two comma three. Choose the Dot tool, the tool that drew it. Press on the dot, drag it to two comma three, and let go. The dot at negative four comma one is extra. Drag it off the graph and let go to remove it. To redraw the whole graph instead, click Clear All. It erases everything so you can start again.

3:32 Keyboard entry instead of drawing

Do you use a keyboard or a screen reader? Is a mouse hard to use? You can type your graph instead of drawing it. From your LMS, start or resume the assignment, then select the More options button at the top of the questions, then User Preferences. Under Drawing Entry, choose Keyboard and text-based drawing entry alternative. Select Update Info, then reload the assignment page. Graph questions now show “Elements to draw:” and an Add new drawing element list in place of the drawing tools.

4:07 Redraw with Clear All

There is no undo. If you need to redraw a graph, click Clear All and draw it again. Your drawing is your answer. Submit the question the same way you submit any other answer. To practice, use the interactive graphing guide. On each example, press the Watch the steps button to see it done. Then press Try it yourself.

The graphing toolbar

Every graphing question has a graph and a row of tools under it. The tools change from question to question, but you use them the same way: pick a tool, then click the graph.

Clear All: Erases everything you drew on that graph so you can draw it again. Use it whenever you need to redraw a graph. There is no undo.
Draw:: The tools this question allows. The shaded tool is the one in use. If more than one looks shaded, click the one you want before you draw. On a number line you can point at a tool to see its name. Coordinate-grid tools show only a picture, so match it to the tool list.
The graph: Click to place points. Most graphs move each click to the nearest grid mark, so you don't need to click exactly on a line.

Pick the tool first, then click the graph. Each shape needs a set number of clicks, in a set order. A parabola starts with its vertex, for example. A shape is finished only after its last click. Clicking outside the graph, even on a button, erases a shape you haven't finished.
To move a point, select the tool that drew it. Then drag the point. The small square handles on a shape only appear while its tool is selected.
To remove one shape, drag one of its points off the graph. Select the tool that drew it first. Let go outside the graph and the shape disappears.
To redraw a graph, click Clear All. It erases everything on that graph so you can start again. There is no undo button.
Your drawing is your answer. Submit the question the same way you submit any other answer.

Number lines

Number line questions use up to three tools: Line segments and rays, Closed dot, and Open dot. Everything you draw stays on the line. Use a closed dot when the number is included: ≤, ≥, or a square bracket [ or ] in interval notation. Use an open dot when it is not included: <, >, or a parenthesis ( or ). A segment that ends on the first or last number of the line gets an arrowhead, which makes it a ray.

Read the steps for Examples 1 to 3

Example 1: graph x ≥ −2 with a dot and a ray

Choose Closed dot and click −2. The filled dot includes −2.
Choose Line segments and rays, then click −2 to start the ray.
Click the last number at the right edge of the example, 10. Check that an arrowhead appears, so the graph continues to the right.

Example 2: graph the interval (−3, 4]

Choose Open dot and click −3. The parenthesis leaves −3 out.
Choose Closed dot and click 4. The bracket includes 4.
Choose Line segments and rays, then click −3 and 4 to join the dots.

Example 3: graph x < −1 or x ≥ 2

Choose Open dot and click −1, then choose Closed dot and click 2.
Choose Line segments and rays. Click −1, then the first number at the left edge of the example, −10. Check for a left arrowhead.
Click 2, then the last number at the right edge, 10. Check for a right arrowhead. Leave the gap between −1 and 2 unshaded.

The interactive example loads when JavaScript is available. You can follow the written steps above and read the video transcripts without it.

The segment and its dots are separate pieces. If you move the end of a segment, move its dot too.

Coordinate grids

On a coordinate grid, each tool draws one kind of shape from the points you click. A line needs two points, a parabola needs its vertex and one more point, and an inequality needs two points on its boundary plus a click on the side to shade.

Read the steps for Examples 4 to 7

Example 4: plot the points (2, 3), (−4, 1) and (0, −5)

Choose the Dot tool first. The example starts with Line selected.
Click (2, 3): from the origin, move 2 right and 3 up.
Click (−4, 1): move 4 left and 1 up. Then click (0, −5), which is 5 down on the vertical axis.

Example 5: graph the line y = 2x − 3

Find two points on the line. When x = 0, y = −3. When x = 2, y = 1.
Choose Line and click (0, −3).
Click (2, 1). The tool draws the whole line through both points; you do not need to add separate dots.

Example 6: graph the inequality y < 2x + 1

Choose Linear inequality, dashed line. The < symbol excludes the boundary; ≤ and ≥ use a solid line.
Click two points on the boundary y = 2x + 1: (0, 1) and (1, 3).
Test (2, 0): 0 < 2 × 2 + 1 is true. Click (2, 0) to shade that side. The graph is finished after this third click.

Example 7: graph the parabola f(x) = (x − 1)² − 4

Choose Parabola.
Click the vertex first: (1, −4).
Click one more point on the parabola: (3, 0), since f(3) = 0. The tool draws the whole parabola.

The interactive example loads when JavaScript is available. You can follow the written steps above and read the video transcripts without it.

Fixing mistakes

There is no undo button. If you need to redraw a graph, click Clear All and draw it again. To fix just one piece, move it or remove it.

Read the steps for Example 8

Example 8: move a point, then remove an extra one

The example asks for (2, 3), but starts with dots at (3, 2) and (−4, 1).

Choose Dot, the tool that drew the points.
Press on (3, 2), drag it to (2, 3), then let go.
Press on the extra point at (−4, 1), drag it off the graph, then let go to remove it.
To start the whole graph again, choose Clear All. It erases all the pieces on that graph.

The interactive example loads when JavaScript is available. You can follow the written steps above and read the video transcripts without it.

On a coordinate grid

Move a point: select the tool that drew it, then drag the point. Dragging one handle of a line or parabola reshapes it.
Remove a shape: select its tool, drag one of its points off the graph, and let go.
Stop a shape halfway: click anywhere outside the graph. The unfinished shape disappears.
Redraw the graph: click Clear All and start again.
Word-button Line: on older questions with a Line word button, its points can’t be dragged off. Use Clear All.

On a number line

Move a dot: select Closed dot or Open dot (whichever you used), then drag it along the line.
Resize a segment or ray: select Line segments and rays, then drag its end. Let go on the line. If you let go past either end, the segment is removed.
Remove a dot: select Closed dot or Open dot (whichever you used), then drag the dot up or down off the number line and let go.
Remove a segment or ray: select Line segments and rays, press on one of its ends (not the middle), and drag it up or down off the number line.
Redraw the graph: click Clear All and start again.

Tool list

Your question shows some of these tools. Click the points in the order shown. A shape is finished after its last click.

Tool	Clicks	What to click, in order
Number line
Line segments and rays	2	The start, then the end. For a ray, make the end the first or last number on the line.
Closed dot	1	The number. Use it when the number is included.
Open dot	1	The number. Use it when the number is not included.
Points and lines
Dot	1	The point.
Open dot	1	The point.
Line	2	Any two points on the line.
Dashed line	2	Any two points on the line.
Line segment	2	The start point, then the end point.
Ray	2	The endpoint, then another point the ray passes through.
Vector	2	The start, then the tip.
Curves
Parabola	2	The vertex, then another point on the parabola.
3 Point Parabola	3	Any three points on the parabola.
Horizontal parabola	2	The vertex, then another point. It opens toward that point.
Half Parabola	2	The vertex, then another point on the half you want.
Absolute value	2	The corner (vertex), then another point on the graph.
Square root	2	The starting point, then another point on the graph.
Cube Root	2	The center (inflection) point, then another point on the graph.
Cubic	2	The center (inflection) point, then another point on the graph.
Circle	2	The center, then a point on the circle.
Ellipse	2	The center, then the corner point that is the horizontal radius across and the vertical radius up or down.
Vertical hyperbola	2	The center, then the point with the co-vertex's x and the vertex's y.
Horizontal hyperbola	2	The center, then the point with the vertex's x and the co-vertex's y.
Rational	2	The point where the two asymptotes cross, then a point on the graph.
Exponential	2	Two points on the graph. The asymptote is the x-axis.
General Exponential	3	A point on the horizontal asymptote, then two points on the graph.
Logarithm	2	Two points on the graph. The asymptote is the y-axis.
General Logarithm	3	A point on the vertical asymptote, then two points on the graph.
Cosine	2	A highest or lowest point, then the next lowest or highest point, half a period later.
Sine	2	A point on the midline, then the next highest or lowest point, a quarter period later.
Tangent	3	The center (inflection) point, a point on a vertical asymptote, then a point on the graph.
Inequalities
Linear inequality, solid line	3	Two points on the boundary line, then a point on the side to shade. Use it for ≤ and ≥.
Linear inequality, dashed line	3	Two points on the boundary line, then a point on the side to shade. Use it for < and >.
Quadratic inequality, solid line	3	The vertex, another point on the parabola, then a point on the side to shade.
Quadratic inequality, dashed line	3	The vertex, another point on the parabola, then a point on the side to shade.
Absolute value inequality, solid line	3	The corner, another point on the graph, then a point on the side to shade.
Absolute value inequality, dashed line	3	The corner, another point on the graph, then a point on the side to shade.
Word buttons (some older questions)
Line	any	Each point in order. The line stays attached to your pointer until you finish it: click the last point again, double-click, or click outside the graph. Its points can't be dragged off the graph, so use Clear All to redraw it.
Line Segment	2	The start point, then the end point.
Dot	1	The point.
Open Dot	1	The point.
Polygon	any	Each corner in order. To close the shape, click the first corner again. If the line still follows your pointer, finish it like the word-button Line.
Freehand Draw	drag	Press and drag to draw, then let go. Freehand strokes can't be moved.
Eraser	1	Click any shape to erase it.

Keyboard entry instead of drawing

The drawing tools work only with a mouse or touch. If you use a keyboard or a screen reader, or a mouse is hard to use, you can type your graph instead of drawing it. Your typed graph is checked by the same grader as a drawn one. A few questions show a keyboard-friendly version instead.

Turn it on

First open your preferences:

From your LMS

Start or resume the assignment, then select the ⋮ More options button at the top of the questions, then User Preferences.

At xyzhomework.com

Select User Settings at the top of the page, or in the menu under your profile icon.

Under Drawing Entry, choose Keyboard and text-based drawing entry alternative.
Select Update Info, then reload the assignment page. Graph questions now show “Elements to draw:” and an Add new drawing element list in place of the drawing tools.

Add each piece of the graph

Under Add new drawing element, choose the element, for example Solid dot or Line, and select Add.
Type its values in the box that appears. The box tells you what to enter, for example “Enter two points on the line”. Coordinate points go in parentheses, with commas between points.
Add the next piece the same way. Use Remove to delete an element. Keyboard entry has no Clear All.

To graph	Choose	Type
Number line
Closed dot at $- 2$	Solid dot	`-2`
Open dot at $4$	Open dot	`4`
Segment from $- 3$ to $4$	Line segment	`-3, 4`
Ray from $- 2$ going right	Ray to the right	`-2`
Ray from $- 1$ going left	Ray to the left	`-1`
Coordinate grid
The point $(2, 3)$	Solid dot	`(2,3)`
The line $y = 2 x - 3$	Line	`(0,-3),(2,1)`
The parabola $f (x) = {(x - 1)}^{2} - 4$	Parabola	`(1,-4),(3,0)`
$y < 2 x + 1$	Linear inequality with dashed line	`(0,1),(1,3),(2,0)`

If the list offers Lines rather than Line, the question wants points joined by straight segments. Type every point in order, for example (-2,-7),(0,-3),(4,5).

If the points aren’t typed the way the box expects, you see “Error: Invalid format for points” or “Error: Incorrect number of points”, followed by what the box expects.

Tablets and phones

You can draw with your finger. Tap a tool, then tap the graph to place each point. To move a point, press and hold it, then drag. To zoom, pinch with two fingers on the page outside the graph. A pinch that starts on the graph can drop a dot or start a segment, so check the graph after zooming.

If a graph doesn’t respond to touch, finish the question on a computer with a mouse, or turn on keyboard entry.

How to answer graphing questions

Watch the how-to graphing videos

Graphing Your Answers

The graphing toolbar

Number lines

Example 1: graph x ≥ −2 with a dot and a ray

Example 2: graph the interval (−3, 4]

Example 3: graph x < −1 or x ≥ 2

Coordinate grids

Example 4: plot the points (2, 3), (−4, 1) and (0, −5)

Example 5: graph the line y = 2x − 3

Example 6: graph the inequality y < 2x + 1

Example 7: graph the parabola f(x) = (x − 1)² − 4

Fixing mistakes

Example 8: move a point, then remove an extra one

On a coordinate grid

On a number line

Tool list

Keyboard entry instead of drawing

Turn it on

From your LMS

At xyzhomework.com

Add each piece of the graph

Tablets and phones

Related

Still stuck?