Question

Which statement correctly compares functions f and g?

function f function g
An exponential function passes through (- 1, 5), and (2, - 1.5) intercepts axis at (1, 0), and (0, 2) Function g is a decreasing exponential function with a y-intercept of 5 and no x-intercept.

A. They have different end behavior as x approaches -[infinity] and different end behavior as x approaches [infinity].
B. They have the same end behavior as x approaches -[infinity] but different end behavior as x approaches [infinity].
C. They have different end behavior as x approaches -[infinity] but the same end behavior as x approaches [infinity].
D. They have the same end behavior as x approaches -[infinity] and the same end behavior as x approaches [infinity].

Answer 1

Function f and function g have different end behaviors as x approaches negative infinity, but the same end behavior as x approaches positive infinity, which is option C.

Step-by-step explanation:

To compare the end behaviors of functions f and g, we must understand the characteristics of exponential functions. Exponential functions can either grow or decay as the input variable x approaches infinity. A function with positive exponents or increasing exponentially will approach infinity as x approaches infinity, and a function with negative exponents or decreasing exponentially will approach zero as x approaches infinity.

Function f is described with two points (-1, 5) and (2, -1.5) and intercepts (1, 0), and (0, 2), suggesting it is not a standard exponential function but may instead be linear or polynomial. Function g is described as a decreasing exponential function with a y-intercept of 5 and no x-intercept, indicating it approaches zero as x approaches infinity.

Given this information, the correct answer is: C. They have different end behavior as x approaches -[infinity] but the same end behavior as x approaches [infinity].