Answer to Question #246491 in Calculus for Lara

Question

Graph each function. Then identify the vertex, two points, domain, and range.

f(x) = |-1/5(x + 5)| + 2

Answer 1

Solution:

The graph of $f(x)=|-\frac{\left(x\:+\:5\right)}{5}|\:+\:2$ is

From the graph:

$\mathrm{Domain\:of\:}\:\frac{\left|x+5\right|}{5}+2\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Range\:of\:}\frac{\left|x+5\right|}{5}+2:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:2\:\\ \:\mathrm{Interval\:Notation:}&\:[2,\:\infty \:)\end{bmatrix}$

Vertex $: (-5,2)$

Two points $:(0,3),(5,4)$