CPM Homework Help : PC Problem 1-80

The 3 section continuous linear piecewise graph, labeled f of x, left horizontal coming from negative infinity at, y = negative 1, turning up at the point (0, comma negative 1), turning horizontal at the point (3, comma 1). function $f\left(x\right)$ is shown below right. Below are functions $g\left(x\right)$ and $h\left(x\right)$ which are transformations of $f\left(x\right)$ . Find expressions for $g\left(x\right)$ and $h\left(x\right)$ in terms of $f\left(x\right)$ . Try this using an eTool.

Describe how the graph is reflected.
Answer (a) graph:
Reflected vertically: $-f\left(x\right)$
Describe the vertical shift.
Answer (a) vertical shift:
Shifted up $3$ units: $f\left(x\right) + 3$
$g\left(x\right) = -f\left(x\right) + 3$

Describe the horizontal shift.
Answer (b) horizontal shift:
Shifted left $1$ unit: $f\left(x + 1\right)$
Describe the vertical shift.
Answer (b) vertical shift:
Shifted up $1$ unit: $f\left(x\right) + 1$
Describe the stretch factor.
Answer (b) stretch factor:
Doubled: $2\left(f\left(x\right)\right)$
$h\left(x\right) = 2f\left(x + 1\right) + 2$