Question

The linear function f(x) = ax-5 has the end behavior as x towards infinity, y towards infinity and x towards negative infinity, y towards negative infinity. Which inequality represents all the possible values of a?

Answer 1

Answer: B

Explanation:

It's a linear function, a line, When x is getting bigger y is going up so it's a positive slope.

a must be a positve number and can't be 0.

so answer is B

Answer 2

The end behavior of the linear function f(x) = ax - 5 tells us that as x approaches infinity, the value of f(x) approaches infinity, and as x approaches negative infinity, the value of f(x) approaches negative infinity.

To determine the possible values of a that satisfy this end behavior, we need to consider the slope of the function.

Since the function is linear, the slope is the coefficient of x, which is a.

If a is positive, then the function will increase without bound as x approaches infinity and decrease without bound as x approaches negative infinity. This matches the end behavior we want, so we know that a > 0.

If a is negative, then the function will decrease without bound as x approaches infinity and increase without bound as x approaches negative infinity. This does not match the end behavior we want, so we can exclude all negative values of a.

Therefore, the inequality that represents all possible values of a is:

a > 0