Question

function g is a vertically scaled version of function f. the functions are graphed where f is solid and g is dashed.
what is the equation of g in terms of f?
choose 1 answer:
a ( g(x) = \frac{1}{3}f(x) )
b ( g(x) = 3f(x) )
c ( g(x) = f(x) + 2 )
d ( g(x) = f(x) - 2 )

Explanation:

Step1: Analyze the vertical scaling

To determine the vertical scaling, we can look at a point on \( f(x) \) and the corresponding point on \( g(x) \). Let's take the y - intercept of \( f(x) \), which is \( (0, 6) \), and the corresponding point on \( g(x) \) is \( (0, 2) \).

Step2: Determine the scaling factor

If \( g(x)=a\times f(x) \), then when \( x = 0 \), \( g(0)=a\times f(0) \). We know that \( f(0) = 6 \) and \( g(0)=2 \). So we solve the equation \( 2=a\times6 \) for \( a \).
\[
a=\frac{2}{6}=\frac{1}{3}
\]
So the equation of \( g(x) \) in terms of \( f(x) \) is \( g(x)=\frac{1}{3}f(x) \)

Answer:

A. \( g(x)=\frac{1}{3}f(x) \)