Answer:
A. The y-intercepts are the same.
B. function [tex]3f(x)[/tex] has a greater rate of change.
Step-by-step explanation:
We have [tex]f(x)=x[/tex]
Let [tex]g(x)=3*f(x)[/tex]
Then [tex]g(x)=3x[/tex]
The y-intercept of [tex]f(x)=x[/tex] is 0
The y-intercept of [tex]g(x)=3x[/tex] is also 0
Therefore the y-intercepts are the same.
The rate of change of [tex]f(x)=x[/tex] is 1
The rate of change of [tex]g(x)=3x[/tex] is 3
Hence the function [tex]3f(x)[/tex] has a greater rate of change.
The two functions are not parallel because they have different rate of change.
f(x) translated 3 units up is f(x)+3. This is not the same as 3x
