Question

the graph of g(x) is created by graphing the equation g(x)=h(x - 5). which transformation on the graph of function h creates the graph of function g? a a vertical shift 5 units upward b a vertical shift 5 units downward c a horizontal shift 5 units to the left d a horizontal shift 5 units to the right

Explanation:

Step1: Recall Function Transformation Rules

For a function \( y = h(x - k) \), the transformation of \( y = h(x) \) is a horizontal shift. If \( k>0 \), it's a shift to the right by \( k \) units; if \( k<0 \), it's a shift to the left by \( |k| \) units. Vertical shifts are of the form \( y = h(x)+k \) (up if \( k>0 \), down if \( k<0 \)).

Step2: Analyze \( g(x)=h(x - 5) \)

Here, the function is \( g(x)=h(x - 5) \), which matches the horizontal shift form \( y = h(x - k) \) with \( k = 5>0 \). So, this is a horizontal shift of the graph of \( h(x) \) 5 units to the right to get \( g(x) \).

Answer:

D. a horizontal shift 5 units to the right