Question

if f(x) = 4x - 2 is vertically translated 6 units up to g(x), what is the y-intercept of g(x)? 4 6 -8 -2

Explanation:

Step1: Recall vertical translation rule

For a function \( f(x) \), a vertical translation up by \( k \) units gives \( g(x)=f(x)+k \). Here, \( f(x) = 4x - 2 \) and \( k = 6 \), so \( g(x)=4x - 2+6 \).

Step2: Simplify \( g(x) \)

Simplify \( g(x) \): \( g(x)=4x + 4 \).

Step3: Find y - intercept

The y - intercept of a linear function \( y=mx + b \) is \( b \). For \( g(x)=4x + 4 \), when \( x = 0 \), \( y=4 \). So the y - intercept is 4.

Answer:

4