Question

The function f(i) = 5(a-1) is shown on the coordinate plane. Select from the drop-down menus to correctly describe the end behavior of f(a):

1. As a approaches [infinity] , the function f(a)...
a. Increases without bound
b. Decreases without bound
c. Approaches a finite limit
d. Exhibits oscillating behavior

2. As a approaches [infinity] , the function f(a)...
a. Increases without bound
b. Decreases without bound
c. Approaches a finite limit
d. Exhibits oscillating behavior

Answer 1

For the function f(a) = 5(a-1), as a approaches infinity, the function increases without bound, corresponding to option a for both questions regarding its end behavior.

Step-by-step explanation:

To determine the end behavior of the function f(a) = 5(a-1), we can analyze it as a approaches infinity. This function is a linear function with a constant rate of change and no asymptotes or bounds. Therefore, as a approaches infinity, the function increases without bound, which corresponds to option a for both questions about the function's end behavior as a approaches infinity.

In terms of the other parts mentioned,

• The graph of f(x) for 0 ≤ x ≤ 20 being a horizontal line is unrelated because we are considering the behavior as x goes to infinity, not within a restricted interval.
• The discussion of y = 1/x having asymptotes provides general knowledge about some functions having limits they cannot cross, which does not apply in this case.
• The mention of a function at x = 3 with certain behaviors does not directly relate to determining the end behavior of a linear function such as f(a) = 5(a-1).