You Try It!

Here are some problems involving absolute value equations in a slideshow. Complete them in your notebook, then click on the reveal answer to check your work.

See if you can graph y = |x|. Start by trying to fill in a table of values. Make sure you go from -5 all the way to 5. Then see if you can plot the points on a graph. Click the reveal answer button for the solution.

The absolute value of a number can be written as that value without the sign. For example, the absolute value of -5 is 5 and the absolute value of +5 is 5.

x	y
-5	5
-4	4
-3	3
-2	2
-1	1
0	0
1	1
2	2
3	3
4	4
5	5

y = |x|

See if you can graph y = |x + 2|. Fill in the table below to find some points to graph. Click on the headers of each column to reveal the values. Then, see if you can plot those values on a graph. Click the answer button below to reveal the solution.

x	x + 2	\|x + 2\|	y
-5	-3	3	3
-4	-2	2	2
-3	-1	1	1
-2	0	0	0
-1	1	1	1
0	2	2	2
1	3	3	3
2	4	4	4
3	5	5	5
4	6	6	6
5	7	7	7

First you add 2 to each value of x, then you remove the sign to equal the absolute value. Notice in the graph below that adding 2 inside the absolute value, |x + 2| shifts the graph 2 units to the left.

See if you can graph y = -2|x|. Fill in the table below to find some points to graph. Click on the headers of each column to reveal the values. Then, see if you can plot those values on a graph. Click the answer button below to reveal the solution.

x	\|x\|	-2 \|x\|	y
-5	5	-10	-10
-4	4	-8	-8
-3	3	-6	-6
-2	2	-4	-4
-1	1	-2	-2
0	0	0	0
1	1	-2	-2
2	2	-4	-4
3	3	-6	-6
4	4	-8	-8
5	5	-10	-10

Order of operations tells you to work inside the grouping symbol, the absolute value symbol, before multiplying. First, find the absolute value of x, and then multiply each by -2.

See if you can graph y = 3 |-2x|. Fill in the table below to find some points to graph. Click on the headers of each column to reveal the values. Then, see if you can plot those values on a graph. Click the answer button below to reveal the solution.

x	-2x	\|-2x\|	y = 3\|-2x\|
-5	10	10	30
-4	8	8	24
-3	6	6	18
-2	4	4	12
-1	2	2	6
0	0	0	0
1	-2	2	6
2	-4	4	12
3	-6	6	18
4	-8	8	24
5	-10	10	30

First, calculate inside the grouping symbol, so multiply (-2)(x). Next find the absolute value |-2x|. Finally, multiply times 3.

See if you can graph y = |x| - 5. What does subtracting 5 to the absolute value of x do to the graph? Fill in the table below to find some points to graph. Click on the headers of each column to reveal the values. Then, see if you can plot those values on a graph. Click the answer button below to reveal the solution.

x	\|x\|	y
-5	5	0
-4	4	-1
-3	3	-2
-2	2	-3
-1	1	-4
0	0	-5
1	1	-4
2	2	-3
3	3	-2
4	4	-1
5	5	0

Subtracting 5 from the absolute value of x shifts the graph down 5.

See if you can graph y = |x| + 6. Fill in the table below to find some points to graph. Click on the headers of each column to reveal the values. Then, see if you can plot those values on a graph. Click the answer button below to reveal the solution.

x	\|x\|	y = \|x\| + 6
-10	10	16
-8	8	14
-6	6	12
-4	4	10
-2	2	8
0	0	6
2	2	8
4	4	10
6	6	12
8	8	14
10	10	16

First, solve for y.
y = |x| + 6.
Next, find the absolute value for each x. Then divide |x| by 4 and add 6 to tne answer.

See if you can graph y > -2|x|. Fill in the table below to find some points to graph. Click on the headers of each column to reveal the values. Then, see if you can plot those values on a graph. Remember to shade the correct area of the graph. Will the line be solid or dotted? Click the answer button below to reveal the solution.

x	\|x\|	y > -2\|x\|
-5	5	-10
-4	4	-8
-3	3	-6
-2	2	-4
-1	1	-2
0	0	0
1	1	-2
2	2	-4
3	3	-6
4	4	-8
5	5	-10

Since y is greater than -2|x| the line is dotted and the graph is shaded above the line:

What is the equation for the function shown on this graph?

y \(\small\mathsf{ \leq }\) |x| + 4

Since the graph is shaded, we know that this is an inequality. The shading is under the line and the line is solid, so we know the equation is "y is less than or equal to". The "v" tells us this equation is an absolute value of x. The "v" is centered on the y-axis and the slope is one, so we know that the equation begins with y \(\small\mathsf{ \leq }\) |x|...
The line is shifted up 4. This tells us that the equation is y \(\small\mathsf{ \leq }\) |x| + 4.

See if you can graph y > -2|x - 3|. Fill in the table below to find some points to graph. Click on the headers of each column to reveal the values. Then, see if you can plot those values on a graph. Remember to shade the correct area of the graph. Will the line be solid or dotted? Click the answer button below to reveal the solution.

x	x - 3	\|x - 3\|	y > -2\|x - 3\|
-5	-8	8	-16
-4	-7	7	-14
-3	-6	6	-12
-2	-5	5	-10
-1	-4	4	-8
0	-3	3	-6
1	-2	2	6
2	-1	1	-2
3	0	0	0
4	1	1	-2
5	2	2	-4

The -3 in |x - 3| shifts the graph 3 to the right:

Now it's your turn to practice graphing with absolute value functions.