Question

16 mark for review the function f is defined by f(x) = (x - 6)(x - 2)(x + 6). in the xy-plane, the graph of y = g(x) is the result of translating the graph of y = f(x) up 4 units. what is the value of g(0)?

Explanation:

Step1: Find f(0)

Substitute \( x = 0 \) into \( f(x)=(x - 6)(x - 2)(x + 6) \).
\( f(0)=(0 - 6)(0 - 2)(0 + 6)=(-6)(-2)(6) \).
Calculate: \( (-6)\times(-2)=12 \), then \( 12\times6 = 72 \). So \( f(0)=72 \).

Step2: Determine g(x) from translation

Translating \( y = f(x) \) up 4 units means \( g(x)=f(x)+4 \).

Step3: Find g(0)

Substitute \( x = 0 \) into \( g(x) \): \( g(0)=f(0)+4 \).
We know \( f(0)=72 \), so \( g(0)=72 + 4=76 \).

Answer:

76