Question

Use the graph of g to answer the questions. Assume the domain of g is [-8,8]. a. g(8) = b. g(-4) = c. For how many values of x does g(x) = -0.1? ______ d. For what value(s) is g = 0? ______ (You can round to nearest half of a unit and enter multiple values separated by commas, if necessary).

Answer 1

Given the graph and knowing that the Domain of the "g" is:

`Domain\colon\mleft[-8,8\mright]`

You need to remember that the x-values are also called input values, and the y-values are also called output values.

a. Notice that you need to find:

`g(8)`

This is the corresponding output value for:

`x=8`

You can use the graph to find it by identifying the corresponding y-coordinate for the x-coordinate 8. See the picture below:

Therefore:

`g(8)=4`

b. Use the same procedure to find:

`g\mleft(-4\mright)`

Whose input value is:

`x=-4_{}`

See the picture below:

Hence:

`g\mleft(-4\mright)=-2`

c. Notice that you have this output value:

`g\mleft(x\mright)=-0.1`

You can identify in the graph that the approximate location of the point that has that y-coordinate is:

Where the red dots represent the points that have this y-coordinate:

`y=-0.1`

Therefore, three x-values have this output value:

`g\mleft(x\mright)=-0.1`

Notice that that point has

d. You can identify that the graph of "g" passes through the Origin:

`(0,0)`

And it intersects the x-axis at:

`\begin{gathered} x=-2 \\ x=2 \end{gathered}`

By definition, the value y-value is zero when the graph intersects the y-axis. Therefore, you can identify that the points that have y-coordinate 0 are:

`(0,0),(-2,0),(2,0)`

Hence, the answers are:

a.

`g(8)=4`

b.

`g\mleft(-4\mright)=-2`

c. For three values.

d.

`\begin{gathered} x=0 \\ x=2 \\ x=-2 \end{gathered}`