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Mazyrski [523]
3 years ago
5

What can you say about the end behavior of the function f(x) = -4x6+6x2 -52 ?

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
5 0

Answer:

A. F(x)is an even function so both ends of the graph go in the same direction.

D. The leading coefficient is negative so the left end of the graph goes down.

Step-by-step explanation:

Even function:

For every value of x, f(x) = f(-x)

In this question:

We are given the following function:

f(x) = -4x^6 + 6x^2 - 52

Testing if it is even:

f(1) = -4(1)^6 + 6(1)^2 - 52 = -4 + 6 - 52 = -50

f(-1) = -4(-1)^6 + 6(-1)^2 - 52 = -4 + 6 - 52 = -50

Since f(1) = f(-1), it is even.

Since it is even, both ends of the graph go in the same direction, so option A is correct, while option B is wrong.

Options C and D:

The leading coefficient, is -4(which multiplies x with the highest exponent). Since it is negative, it goes to negative infinity as x increases, that is, the left end goes down, and option D is correct while C is not.

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6 0
3 years ago
<img src="https://tex.z-dn.net/?f=n%20-%205%20%5Cleqslant%205n%20-%201" id="TexFormula1" title="n - 5 \leqslant 5n - 1" alt="n -
ANTONII [103]
Hello there!

n - 5 ≤ 5n - 1

Solve for n

Let's start by subtracting 5n from both sides

n - 5 - 5n ≤ 5n - 5n - 1

n - 5 - 5n ≤ -1

We need to transfer -5 on the other side, we can do that by adding 5 on both sides

n - 5 - 5n + 5 ≤ -1 + 5

n - 5n ≤ -4

-4n ≤ -4

Finally divide both sides by -4

-4n/-4 ≤ -4/-4

n ≥ -1   (This is the answer)!

Do you know why I changed the sign?


 A lot of students failed to remember that rules, which is:
When you are solving an inequality, if you divide both sides by a negative sign, you MUST change the symbol as well. If it was this <, it will change to this >. Got it? Cool!



I hope the steps are clear to understand. If you have questions, feel free to let me know...

As always, I am here to help!
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