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

As $$x \to \pm \infty$$, $$f(x) \to -\infty$$

Question 1

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

Accepted Answer

Question 2

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

Accepted Answer

$$x = -1$$

Question 3

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

Accepted Answer

$$6.125$$ feet

Question 4

Consider $$f(x) = 4x^2$(x-3)^2(x+2$$)$. Which zero has even multiplicity?

Accepted Answer

$$x = 0$$

Question 5

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

Accepted Answer

As $$x 	o \pm \infty$$, $$f(x) 	o -\infty$$

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 statement is correct?

Accepted Answer

$$f(0)  0$$, so a zero exists between 0 and 1.

Question 7

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

Accepted Answer

$$7$$

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

For the rational function $$f(x) = \frac{x^3$ - 2x^2$ - 8x}{x^2$ - 16}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 4$$ and $$x = -4$$

Question 10

For $$f(x) = \frac{2x-5}{x^2$ - 5x + 4}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 11

Solve the inequality $$2x^2 + 5x - 3$$ \u003c 0$$. What is the solution in interval notation?

Accepted Answer

$$(-3, 0.5)$$

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

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

Question 16

Condense $$3\log_5$ y - \log_5$ z$$ into a single logarithm with coefficient 1.

Accepted Answer

$$\log_5$ \frac{y^3$}{z}$$

Question 17

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

Accepted Answer

$$x = -\frac{1}{2}$$

Question 18

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

Accepted Answer

$$28,212.13$$

Question 19

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

Accepted Answer

$$1,277$$ years

College Algebra Review: Quadratic, Polynomial, Rational, Exponential, and Logarithmic Functions

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