Question

below is the graph of ( f(x)=2ln(x) ). how would you describe the graph of ( g(x)=4ln(x) )?

a. ( g(x) ) shifts ( f(x) ) up 2 units.
b. ( g(x) ) shifts ( f(x) ) to the right 2 units.
c. ( g(x) ) compresses ( f(x) ) by a factor of 2.
d. ( g(x) ) stretches ( f(x) ) vertically by a factor of 2.

Explanation:

The function \( g(x) = 4\ln(x) \) can be written as \( g(x) = 2 \cdot [2\ln(x)] = 2f(x) \). A transformation of the form \( y = kf(x) \) where \( k > 1 \) results in a vertical stretch of the graph of \( f(x) \) by a factor of \( k \). Here, \( k = 2 \), so \( g(x) \) is a vertical stretch of \( f(x) \) by a factor of 2.

Answer:

D. \( g(x) \) stretches \( f(x) \) vertically by a factor of 2.