Question

For each absolute value equation , list characteristics. I’m stuck on b. I’m not sure if it’s a horizontal stretch or horizontal shrink.

Answer 1

Given:

$y=-\lvert\frac{1}{3}x-2\rvert+9$

For the absolute value equation,

$\begin{gathered} f(x)=a|bx-h|+k \\ a\text{ denote the graph shrinks or stretched} \\ h\text{ denote graph goes left or right} \\ k\text{ denote graph goes up or down} \\ b\text{ denote the horizontal stretched or shrink} \end{gathered}$

So, the given equation,

The graph is reflected over x-axis. since, f(x) = -f(x).

$b=\frac{1}{3}<1\Rightarrow\text{ horizontal stretched}$

The graph is 6 units right and 9 units up.