Question

question 5 of 40
which statements describe one of the transformations performed on
$f(x) = x^2$ to create $g(x) = 2x^2 + 5$? choose all that apply.

a. a translation of 5 units to the right
b. a vertical stretch with a scale factor of 2
c. a translation of 5 units up
d. a vertical stretch with a scale factor of $\frac{1}{2}$

Explanation:

Step1: Analyze vertical scaling

The coefficient of $x^2$ in $g(x)$ is 2. A coefficient $a>1$ outside the base function causes vertical stretch by factor $a$. So $2x^2$ is vertical stretch by 2.

Step2: Analyze vertical translation

The $+5$ at the end of $g(x)$ is a constant added to the function. A constant $k>0$ added to the function translates it up by $k$ units. So $+5$ is translation up by 5.

Answer:

B. A vertical stretch with a scale factor of 2, C. A translation of 5 units up