Question

what kind of transformation converts the graph of f(x) = 2x + 7 into the graph of g(x) = 2x + 4?
translation 3 units left
translation 3 units up
translation 3 units right
translation 3 units down

Explanation:

Step1: Analyze the functions

The function \( f(x) = 2x + 7 \) and \( g(x)=2x + 4 \). The general form of a vertical translation of a function \( y = f(x) \) is \( y=f(x)+k \), where \( k>0 \) is up and \( k < 0 \) is down.

Step2: Find the difference

We can write \( g(x)=f(x)+(4 - 7)=f(x)- 3 \). Comparing with \( y = f(x)+k \), here \( k=- 3 \). So this is a translation of 3 units down.

Answer:

translation 3 units down