Question

PLEASE HELP Comparing Exponential Functions: Mastery Test

Select all the correct answers. Exponential function f is represented by the table.
X 0 1 2 3 4
f(x) -12 -4 0 2 3
Function g is represented by the equation. g(x) = -12 (1/3)^x
Which statements are true about the two functions?
Both functions are increasing on all intervals of x.
Both functions approach the same value as x approaches infinity
The functions have the same y-intercept.
Both functions approach - as x approaches -infinity The functions have the same x-intercept​

Answer 1

Both functions have the same y-intercept at -12, but they differ in terms of their behavior as x approaches infinity. Function g is decreasing, while f increases and their approaches to infinity cannot be determined without further data.

Step-by-step explanation:

To compare the exponential functions f and g, we need to analyze the properties given by the table of values for f(x) and the equation for g(x). Starting with g(x), we can say that it has a y-intercept of -12 because when x is 0, g(0) = -12. The function g is clearly decreasing since it's raised to a negative exponent (as the base 1/3 is less than 1). As x approaches infinity, g(x) approaches zero because the base 1/3 to the power of infinity becomes very small (not negative infinity as one of the statements suggests). Now, let's look at the table for f(x). At x = 0, f(x) = -12, which means f also has a y-intercept of -12. The function f seems to increase as x increases, and we have to determine if it is increasing at all intervals. This is indeed true since each subsequent y-value is greater than the previous one. However, without more information, we are unable to determine the exact behavior of f as x approaches infinity or whether it has an x-intercept without assuming it is purely exponential. Therefore, the only true statements are that both functions have the same y-intercept.