Answer:
Option (b) is correct.
\(f(x)=\frac{3}{4}|x|\)
Step-by-step explanation:
Given: The parent function \(f(x)=|x|\)
We have to find the equation of the new function when given that the absolute parent function is vertically compress by multiplying by \(\frac{3}{4}\)
Since, given the absolute function \(f(x)=|x|\)
Since, The graph is multiplied by \(\frac{3}{4}\)
Vertically compressed or stretched
For any graph y = f(x),
A vertically compression (stretched) of a graph is compressing the graph toward x- axis.
• if k > 1 , then the graph y = k• f(x) , the graph will be vertically stretched by multiplying each y coordinate by k.
• if 0 < k < 1 if 0 < k < 1 , the graph is f (x) vertically shrunk by multiplying each of its y-coordinates by k.
• if k should be negative, the vertical stretch or shrink is followed by a reflection across the x-axis.
Here, the fraction \(\frac{3}{4}=0.75\) so, the graph is f (x) vertically shrunk by multiplying each of its y-coordinates by k.
That is The new function when given that the absolute parent function is vertically compress by multiplying by \(\frac{3}{4}\) is \(f(x)=\frac{3}{4}|x|\)
