Question

1. if the function $f(x)=x$ is the parent function, describe the transformations of $g(x)=3x + 1$ from the parent function.

a vertical shrink by a factor of $\frac{1}{3}$, vertical translation up 1
b reflection in the $y$-axis
c vertical stretch by a factor of 3, vertical translation up 1
d reflection in the $x$-axis
e horizontal translation left 1

Explanation:

Step1: Identify transformation form

For $g(x)=af(x)+k$, $a$ stretches/shrinks, $k$ translates.

Step2: Match to given functions

Here $f(x)=x$, $a=3$, $k=1$.

Step3: Interpret $a=3$

$a>1$ means vertical stretch by 3.

Step4: Interpret $k=1$

Positive $k$ means shift up 1 unit.

Answer:

C. vertical stretch by a factor of 3, vertical translation up 1