Question

The graphs below are both absolute value functions. The equation of the redgraph is f(x) = |xl. Which of these is the equation of the blue graph, g(x)?f(x) = x 1y5-g(x) = ?-55O A. g(x) = ZHB. g(x) = (x - 21C. g(x) = 5x + 21D. g(x) = 2x

Answer 1

ANSWER

$\Rightarrow y=\frac{1}{2}|x|$

EXPLANATION

We want to find the absolute value function for the line in blue.

The general form of an absolute value function is:

$y=a|x-h|+k$

where (h, k) = vertex

From the line, the vertex of the graph in blue is:

$(0,0)$

To find a, we have to pick a point (x, y) on the line and input it into the general function.

Let us pick (2, 1).

Therefore, we have:

$\begin{gathered} 1=a|2-0|+0 \\ 1=a|2|=2a \\ \Rightarrow a=\frac{1}{2} \end{gathered}$

Therefore, the absolute value function is:

$\begin{gathered} y=\frac{1}{2}|x-0|+0 \\ \Rightarrow y=\frac{1}{2}|x| \end{gathered}$