### Instruction: The range of the function $f(x)$ is $[-3,5].$  Let $h(x) = 2f(x) - 7.$  Find the range of the function $h(x).$.### Response: I need to find the set of possible values that $h(x)$ can take, given the set of possible values that $f(x)$ can take.
I can use the definition of $h(x)$ to relate the two functions.
For any value of $x$, I have $h(x) = 2f(x) - 7.$
This means that whatever $f(x)$ is, $h(x)$ is twice that, minus seven.
So, if $f(x)$ is at its lowest possible value, $-3$, then $h(x)$ is twice that, minus seven, which is $-13$.
Similarly, if $f(x)$ is at its highest possible value, $5$, then $h(x)$ is twice that, minus seven, which is $3$.
Therefore, the range of $h(x)$ is from $-13$ to $3$, or $[-13, 3]$.