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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?


f(x)=(2x^2 + 5)(x - 7)

Select all that apply.

• -3
• 0.2x
• 5x²

-(1)/(2)(x + 8)
• 4(2x - 7)

User Esac
by
8.9k points

2 Answers

5 votes

Answer:

3rd and 4th Choices.


\displaystyle 5x^2\text{ and } -(1)/(2)(x+8)

Explanation:

We are given the function:


f(x)=(2x^2+5)(x-7)

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:


2x^2(x)=2x^3

Thus:


2(-\infty)^3\Rightarrow -\infty

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
0.2x.


0.2(-\infty)\Rightarrow -\infty

This will also make f increase.

The third factor is:


5(\infty)^2\Rightarrow \infty

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

The fourth factor is:


\displaystyle -(1)/(2)(-\infty+8)\Rightarrow -(1)/(2)(-\infty)\Rightarrow \infty

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

Lastly, the fifth factor is:


4(2(-\infty)-7)\Rightarrow 4(-\infty)\Rightarrow -\infty

This is negative, so it will make f increasing.

Therefore, our answers are the third and fourth choices.

User Tadiwanashe
by
7.8k points
9 votes

Answer:

5x²

-1/2( x+8)

Explanation:

The dominant term is 2x^2 *x or 2x^3

We want to know what happens when x goes to negative ∞

2 ( -∞) ^3 → 2 * (-∞) → -∞

As long as we multiply by a positive number, we will still be approaching negative infinity ( or decreasing)

-3 is negative

.2x is negative when x approaches negative infinity

.5 x^2 = .5( -∞)^2 = 5 ( ∞) = ∞ which is positive

-1/2 x is the dominant term = -1/2(- ∞) = ∞ which is positive

4(2x) is the dominant term = 8(- ∞) = - ∞ which is negative

User JonatanE
by
7.8k points

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