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dezoksy [38]
3 years ago
5

What is the end behavior of the graph of f(x) = x5 – 8x4 + 16x3?

Mathematics
2 answers:
ryzh [129]3 years ago
7 0

Answer:

Step-by-step explanation:

f(x) = x⁵ – 8x⁴ + 16x³

As x approaches +∞, the highest term, x⁵, approaches +∞.

As x approaches -∞, x⁵ approaches -∞ (a negative number raised to an odd exponent is also negative).

Now let's factor:

f(x) = x³ (x² – 8x + 16)

f(x) = x³ (x – 4)²

f(x) has roots at x=0 and x=4.  x=4 is a repeated root (because it's squared), so the graph touches the x-axis but does not cross at x=4.

The graph crosses the x-axis at x=0.

jeyben [28]3 years ago
7 0

Answer:

The graph touches, but does not cross, the x–axis at x = .4

The graph of the function crosses the x–axis at x = .0

Step-by-step explanation:

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Ms. Cassidy plotted the point (2, 3) on Miguel’s graph of y < 2x – 4. She instructed him to change one number or one symbol i
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Ms. Cassidy instructed Miguel to change one sign of the graph of y < 2x – 4 so that point (2, 3) can be included in the solution set.

To check which of the given options might Miguel write we check the inequality that holds true for the point (2,3).Substituting x=2 ,y=3 we have:

1) y < 2x – 1

3<2(2)-1

3<3  Not True.

2)y ≤ 2x – 4

3≤ 2(2) -4

3≤ 0  .Not true.

3) y > 2x – 4

3> 2(2)-4

3> 0   True.

4) y < 2x + 4

3<2(2)+4

3<8   True

5) .y < 3.5x – 4

3< 3.5(2)-4

3<3  Not true

6) y < 4x – 4

3<4(2)-4

3<4   True.

Options 3 ,4 ,6 holds true for the point (2,3)


8 0
3 years ago
Read 2 more answers
10. The perimeter of a regular nonagon is 162 inches. The apothem is 97.8 inches. Find the area.
Katen [24]

Answer:

The area of the regular nonagon is 7921.8 square inches.

Step-by-step explanation:

Geometrically speaking, the area of a regular polygon is determined by following area formula:

A = \frac{p\cdot a}{2} (1)

Where:

A - Area of the regular polygon, in square inches.

p - Perimeter, in inches.

a - Apothem, in inches.

If we know that p = 162\,in and a = 97.8\,in, then the area of the regular nonagon is:

A = 7921.8\,in^{2}

The area of the regular nonagon is 7921.8 square inches.

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3 years ago
I also need help with this please it the second question
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true

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3 years ago
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