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

`\Rightarrow y=(1)/(2)|x|`

Step-by-step 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=(1)/(2) \end{gathered}`

Therefore, the absolute value function is:

`\begin{gathered} y=(1)/(2)|x-0|+0 \\ \Rightarrow y=(1)/(2)|x| \end{gathered}`