Which factor could be multiplied by the given function so that their product causes the graph of f(x) to decrease as x approaches negative infinity?

Select all that apply.

• -3
• 0.2x
• 5x²
•
• 4(2x - 7)

3rd and 4th Choices.

Step-by-step explanation:

We are given the function:

And we want to determine the factor(s) that we can multiply to the above function that will cause the graph of f to decrease as x approaches negative infinity.

We can see that the dominant term will be:

Thus:

It is already decreasing (shifting towards negative infinity) as x approaches negative infinity.

In order to preserve this, then, the factors must be positive as x approaches negative infinity.

The first factor is -3.

-3 is always negative, so it will make f increase.

The second factor is .

This will also make f increase.

The third factor is:

This is positive, so it will allow f to remain decreasing as x approaches negative infinity.

The fourth factor is:

This is also positive, so it will also allow f to remain decreasing.

Lastly, the fifth factor is:

This is negative, so it will make f increasing.

Therefore, our answers are the third and fourth choices.