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.

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