Question

What is the end behavior of f(x) = –0.45x + 3?

a) As x decreases without bound, f(x) decreases without bound.
As x increases without bound, f(x) approaches the line y = 3.

b) As x decreases without bound, f(x) increases without bound.
As x increases without bound, f(x) approaches the line y = 3.

c) As x decreases without bound, f(x) approaches the line y = 3.
As x increases without bound, f(x) decreases without bound.

d) As x decreases without bound, f(x) approaches the line y = 3.
As x increases without bound, f(x) increases without bound.

Answer 1

The end behavior of the function f(x) = -0.45x + 3 is as x decreases without bound, f(x) decreases without bound. As x increases without bound, f(x) approaches the line y = 3.

Step-by-step explanation:

The end behavior of a function can be determined by looking at the leading term of the function, which is the term with the highest degree.

In the function f(x) = -0.45x + 3, the leading term is -0.45x.

As x increases or decreases without bounds, the value of -0.45x becomes increasingly large in magnitude. The function approaches negative infinity as x decreases without a bound, and approaches positive infinity as x increases without a bound.

Therefore, the correct answer is a) As x decreases without a bound, f(x) decreases without a bound. As x increases without bound, f(x) approaches the line y = 3.

Answer 2

End behavior is in which direction the ends of the graphs point
All this is just a graph with a negative slope, easy
Instead of a regular graph were both x and y increase, now as x DECREASES, y increases
Without bound means without limits so it's B)