### Home > PC > Chapter 1 > Lesson 1.2.2 > Problem1-80

1-80.

The 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.

1. Describe how the graph is reflected.

Reflected vertically: $-f\left(x\right)$

Describe the vertical shift.

Shifted up $3$ units: $f\left(x\right) + 3$
$g\left(x\right) = -f\left(x\right) + 3$

1. Describe the horizontal shift.

Shifted left $1$ unit: $f\left(x + 1\right)$

Describe the vertical shift.

Shifted up $1$ unit: $f\left(x\right) + 1$

Describe the stretch factor.

Doubled: $2\left(f\left(x\right)\right)$
$h\left(x\right) = 2f\left(x + 1\right) + 2$