Answer:
Option (b) is correct.
[tex]f(x)=\frac{3}{4}|x|[/tex]
Step-by-step explanation:
Given: The parent function [tex]f(x)=|x|[/tex]
We have to find the equation of the new function when given that the absolute parent function is vertically compress by multiplying by [tex]\frac{3}{4}[/tex]
Since, given the absolute function [tex]f(x)=|x|[/tex]
Since, The graph is multiplied by [tex]\frac{3}{4}[/tex]
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 [tex]\frac{3}{4}=0.75[/tex] 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 [tex]\frac{3}{4}[/tex] is [tex]f(x)=\frac{3}{4}|x|[/tex]
