Question

1. if f(x) = x², which function is the result of shifting f(x) by 5 units right and 3 units up? (x + 5)² - 3 (x - 5)² - 3 (x + 5)² + 3 (x - 5)² + 3

Explanation:

Step1: Recall horizontal shift rule

For a function \( y = f(x) \), shifting right by \( h \) units gives \( y = f(x - h) \). Here, \( h = 5 \), so \( f(x - 5)=(x - 5)^2 \).

Step2: Recall vertical shift rule

Shifting up by \( k \) units gives \( y = f(x - h)+k \). Here, \( k = 3 \), so add 3 to the horizontally shifted function: \( (x - 5)^2+3 \).

Answer:

\((x - 5)^2 + 3\) (the last option)