Question

Answer the questions about the following function.

Answer 1

Answer:

Step-by-step explanation:

(a) The function ...

  $f(x)=\dfrac{16x^{2}}{x^{4}+64}$

can be evaluated for x=-2√2 to get ...

  $\displaystylef(-2\sqrt{2})=\frac{16(-2\sqrt{2})^{2}}{(-2\sqrt{2})^4+64}=\frac{128}{64+64}=1$

The point (-2√2, 1) is on the graph of f(x).

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(b) Likewise, we can evaluate for x=2:

  $f(2)=\dfrac{16\cdot 2^2}{2^4+64}=\dfrac{64}{80}=0.8$

The point on the graph is (2, 0.8).

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(c) From part (a), we know that f(-2√2) = 1. Since the function is even, this means that f(2√2) = 1. The graph is a maximum at those points, so there are no other values for which f(x) = 1.

The points (±2√2, 1) are on the graph.

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(d) There are no values of x for which f(x) is undefined. The domain is all real numbers.

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(e) The only x-intercept is at the origin, (0, 0). The x-axis is a horizontal asymptote.

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(f) The only y-intercept is at the origin, (0, 0).

Answer 2

Answer:

its B

Step-by-step explanation: