Exercise 7 Page 103

The graph of $f(x)=0.5x-1$ is shown below.

Let's first consider all of the possible transformations before we graph $g(x)$ and $h(x).$

Now we can start with the graph of $g(x).$

Graph of $g(x)$

To graph it, we should first choose two points on $f(x).$

Next, we will add $2$ to the $y\text{-}$variables of $f(x)$ to translate it up.

Next, we will multiply the $y\text{-}$variables by $2$ to stretch it vertically.

Finally, we will remove the unnecessary parts.

Graph of h(x)

This time, we will start with multiplying the $y\text{-}$coordinates of the line by $2$ to stretch it.

Now we will translate the graph by adding $2$ to its $y\text{-}$variables.

By removing the unnecessary parts, we can finish the graphing.

Combining Graphs

Let's draw the graph of each function on the same coordinate plane and compare them.

When we look at their $y\text{-}$intercepts, we can see that $g(x)$ is the graph of $h(x)$ translated $2$ units up.