Question

3 select the correct answer. which statement correctly compares the graph of function g with the graph of function f? f(x)=e^x - 4 g(x)=1/2e^x - 4 a. the graph of function g is a vertical compression of the graph of function f. b. the graph of function g is a horizontal shift of the graph of function f to the left. c. the graph of function g is a vertical stretch of the graph of function f. d. the graph of function g is a horizontal shift of the graph of function f to the right.

Explanation:

Step1: Recall function - transformation rules

For a function \(y = af(x)+k\), when \(0 < a<1\), it is a vertical compression of \(y = f(x)\). Here, \(f(x)=e^{x}-4\) and \(g(x)=\frac{1}{2}e^{x}-4\), where \(a = \frac{1}{2}\) and \(k=-4\) is the same for both functions.

Step2: Analyze the transformation

Since \(a=\frac{1}{2}\) (where \(0 <\frac{1}{2}<1\)), the graph of \(g(x)\) is a vertical - compression of the graph of \(f(x)\) by a factor of \(\frac{1}{2}\).

Answer:

A. The graph of function \(g\) is a vertical compression of the graph of function \(f\).