Question

which of the following statements are true? graph of two functions f(x) and g(x) is shown a. both graphs are logarithmic functions. b. both graphs have exactly one asymptote. c. both graphs have been shifted and flipped. d. both graphs are exponential functions.

Explanation:

Step1: Analyze Option A

Logarithmic functions have a vertical asymptote and increase/decrease slowly. The red graph looks exponential (increasing, smooth), blue looks like a transformed exponential or maybe a piecewise, not both logarithmic. So A is false.

Step2: Analyze Option B

The red graph (exponential-like) has a horizontal asymptote (y=2 maybe? From the flat part). The blue graph has a vertical asymptote (x=8? The vertical line it approaches). So each has one asymptote. B seems true.

Step3: Analyze Option C

Flipping would reflect over an axis. The red is increasing, blue is maybe a right-shifted and maybe flipped? But red doesn't look flipped. So C is false.

Step4: Analyze Option D

Exponential functions have horizontal asymptotes (for standard ones) or transformations. The blue graph has a vertical asymptote, which exponential functions don't (they have horizontal). So D is false.

Answer:

B. Both graphs have exactly one asymptote.