Question

Make a table of values for the equation, then graph the equation. Y=|x+2|-1

Complete the table below.

Answer 1

A table of values for the equation should be completed as follows;

x y

-5 2

-3 0

-1 0

0 1

1 2

3 4

5 6

In order to use the given absolute value function y = |x + 2| - 1 to complete the table, we would have to substitute each of the values of x (x-values) into the absolute value function and then evaluate as follows;

When the value of x is -5, the absolute value function is given by;

y = |x + 2| - 1

y = |-5 + 2| - 1

y = 2.

When the value of x is -3, the absolute value function is given by;

y = |x + 2| - 1

y = |-3 + 2| - 1

y = 0.

When the value of x is -1, the absolute value function is given by;

y = |x + 2| - 1

y = |-1 + 2| - 1

y = 0.

When the value of x is 0, the absolute value function is given by;

y = |x + 2| - 1

y = |0 + 2| - 1

y = 1.

When the value of x is 1, the absolute value function is given by;

y = |x + 2| - 1

y = |1 + 2| - 1

y = 2.

When the value of x is 3, the absolute value function is given by;

y = |x + 2| - 1

y = |3 + 2| - 1

y = 4.

When the value of x is 5, the absolute value function is given by;

y = |x + 2| - 1

y = |-1 + 2| - 1

y = 6.

Answer 2

Table shown below

Explanation:

Absolute Value Function

The absolute value of any number is the unsigned magnitude of the number. For example,

`|-5|=5`

`|8|=8`

`|-2.3|=2.3`

For any more complex expression, we just take the absolute value where indicated, and then proceed with the rest of the calculations

We are given the function

`y=|x+2|-1`

And we need to compute the values of y for some values of x and complete the table

For x=-5

`y=|-5+2|-1=|-3|-1=3-1=2`

For x=-3

`y=|-3+2|-1=|-1|-1=1-1=0`

For x=-1

`y=|-1+2|-1=|1|-1=1-1=0`

For x=0

`y=|0+2|-1=|2|-1=2-1=1`

For x=1

`y=|1+2|-1=|3|-1=3-1=2`

For x=3

`y=|3+2|-1=|5|-1=5-1=4`

For x=5

`y=|5+2|-1=|7|-1=7-1=6`

The table is shown below