Question

what kind of transformation converts the graph of f(x) = 8x + 2 into the graph of g(x) = 8x + 10?
translation 8 units up
translation 8 units left
translation 8 units right
translation 8 units down

Explanation:

Step1: Analyze Function Forms

The functions are linear: \( f(x) = 8x + 2 \) and \( g(x) = 8x + 10 \). For linear functions \( y = mx + b \), the \( b \)-value (y - intercept) determines vertical position.

Step2: Compare y - Intercepts

The y - intercept of \( f(x) \) is 2, and of \( g(x) \) is 10. The difference is \( 10 - 2=8 \). A positive change in the y - intercept (from 2 to 10) means the graph moves up by 8 units.

Answer:

translation 8 units up