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Diano4ka-milaya [45]
1 year ago
15

The graphs below are both absolute value functions. The equation of the redgraph is f(x) = |xl. Which of these is the equation o

f 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
Mathematics
1 answer:
grigory [225]1 year ago
3 0

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}

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