Q: Given $$f(x) = 25x^2$ - x^4$, what is the end behavior of the graph?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Given the quadratic function $$f(x) = -2x^2$ + 8x$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 8)$$

Question 2

For the function $$f(x) = 3x^2$ + 6x - 9$$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = -1$$

Question 3

A ball is thrown and its height is modeled by $$f(x) = -0.1x^2$ + 1.5x + 5$$, where $$x is $$the horizontal distance in feet. What is the maximum height the ball reaches?

Accepted Answer

$$8.125$$ feet

Question 4

Consider the polynomial $$f(x) = 4x^2$(x-3)^2(x+2$$)$. Which of the following correctly lists the zeros and their multiplicities?

Accepted Answer

$$x=0 ($$multiplicity 2), $$x=3 ($$multiplicity 2), $$x=-2 ($$multiplicity 1)

Question 5

Given $$f(x) = 25x^2$ - x^4$, what is the end behavior of the graph?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 6

Use the Intermediate Value Theorem to show that $$f(x) = -x^2$ + 6x - 1$$ has a zero between $$x=0$$ and $$x=1. $$Which calculation supports this?

Accepted Answer

$$f(0) = -1$$, $$f(1) = 4$$; since $$f(0)  0$$, there is a zero between 0 and 1.

Question 7

Divide $$5x^3$$ - $$6x^2 + 3x + 11$ by x - 2$ using synthetic or long division. What is the remainder?

Accepted Answer

$$9$$

Question 8

Let $$f(x) = x^4$ - 47x^2$ - 15x + 20. $$According to the Remainder Theorem, what is $$f(7)$$?

Accepted Answer

$$f(7) is $$the remainder when $$f(x) is $$divided by $$x-7$$

Question 9

Given $$f(x) = x^3$ - 2x^2$ - 8x \over x^2$ - 16$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(-\infty, -4) \cup (-4, 4) \cup (4, \infty)$$

Question 10

For the rational function $$f(x) = \frac{2x-5}{x^2$ - 5x + 4}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 11

Solve the inequality $$\frac{x-6}{x+2} \u003e 0. $$What is the solution set?

Accepted Answer

$$(-\infty, -2) \cup (6, \infty)$$

Question 12

Rewrite $$e^{2x} = y$ in logarithmic form.

Accepted Answer

$$2x = \ln y$$

Question 13

Evaluate $$\log_2$ 32$$ without a calculator.

Accepted Answer

$$5$$

Question 14

What is the domain of $$f(x) = \log_3$(7 - x)$$?

Accepted Answer

$$(-\infty, 7)$$

Question 15

Expand $$\ln(\sqrt{x(x+1)}) as $$much as possible.

Accepted Answer

$$\frac{1}{2}\ln x + \frac{1}{2}\ln(x+1)$$

Question 16

Condense $$3\log_5$ y - \log_5$ z$$ into a single logarithm with a coefficient of one.

Accepted Answer

$$\log_5$\left(\frac{y^3$}{z}\right)$$

Question 17

Solve for $$x$$: $$8^x = 24$$^{x+1}$$.

Accepted Answer

$$x = -1$$

Question 18

You invest $$12,000 at$$ $$3.4\%$$ annual interest compounded semiannually. What is the accumulated value after $$25$$ years? (Round to the nearest cent.)

Accepted Answer

$$28,489.13$$

Question 19

The exponential decay model for carbon-14 is $$A = A_0$ e$$^{-0.000121t}$$. If a sample contains 85$$\%$$ of the expected amount of carbon-14, estimate the age of the sample to the nearest year.

Accepted Answer

$$1,353$$ years

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