Question

The graphs below are both absolute value functions. The equation of the redgraph is f(x) = [x]. Which of these is the equation of the blue graph, g(x)?fx) = x1y5-Xg(x) = ?-55-5O A. g(x) = 1/4O B. g(x) = (x - 21O C. g(x) = (x + 21O D. g(x) = 21x1

Answer 1

Let's begin by listing out the information given to us:

$\begin{gathered} RedGraph\colon f\mleft(x\mright)=|x| \\ \Rightarrow y=|x| \end{gathered}$

For the Blue Graph, let's pick 4 coordinates along the line to determine the equation of the graph"

$\begin{gathered} (x,y)=(-2,1),(0,0),(2,1),(4,2) \\ |x|=2y\Rightarrow y=\frac{1}{2}|x| \end{gathered}$

We will proceed thus:

$\begin{gathered} y=\frac{1}{2}|x| \\ g(x)=\frac{1}{2}|x| \\ when,x=-2 \\ g(-2)=\frac{1}{2}|-2|=1 \\ when,x=0 \\ g(0)=\frac{1}{2}|0|=0 \\ when,x=2 \\ g(2)=\frac{1}{2}|2|=1 \\ when,x=4 \\ g(4)=\frac{1}{2}|4|=2 \\ \\ \therefore g(x)=\frac{1}{2}|x| \end{gathered}$