Question 1

Given the function $$f(x) = 5x + 8$$, what is the equation for its inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 8}{5}$$

Question 2

Find the inverse of the function $$f(x) = \frac{3x + 4}{2x + 1}.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 1}{3 - 2x}$$

Question 3

For the quadratic function $$f(x) = -3(x - 2)^2$ + 5$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, 5)$$

Question 4

Given $$f(x) = -x^2$ + 6x - 4$$, does the function have a maximum or minimum value, and what is the value?

Accepted Answer

Maximum at $$x = 3$$, value $$f(3) = 5$$

Question 5

What is the degree of the polynomial $$x^3$$ + $$2x^2 - 5x - 6$?

Accepted Answer

3

Question 6

What is the leading coefficient of the polynomial $$x^3$$ + $$2x^2 - 5x - 6$?

Accepted Answer

1

Question 7

Find the $$x-$$intercepts of the polynomial $$x^3$$ + $$2x^2 - 5x - 6$.

Accepted Answer

$$x = -3, x = -1, x = 2$$

Question 8

Divide $$x^2$$ + $$2x^2 - 5x - 6$ by x + 1$ using synthetic division. What is the quotient?

Accepted Answer

Question 9

Write a third-degree polynomial function with real coefficients that has zeros at $$x = -3$$, $$x = 1$$, and $$x = 5.$$

Accepted Answer

$$f(x) = (x + 3)(x - 1)(x - 5)$$

Question 10

Find the vertical asymptotes of $$f(x) = \frac{x+4}{x-2}.$$

Accepted Answer

$$x = 2$$

Question 11

Find the vertical asymptotes of $$f(x) = \frac{x^2$+3x}{x^2$-9}.$$

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 12

Find the vertical asymptotes of $$f(x) = \frac{x^2$-5}{x^2$-3}.$$

Accepted Answer

$$x = \sqrt{3}$$ and $$x = -\sqrt{3}$$

Question 13

Find the horizontal asymptote of $$f(x) = \frac{2x^2$+4}{x^2$-1}.$$

Accepted Answer

$$y = 2$$

Question 14

Find the horizontal asymptote of $$f(x) = \frac{5x^2$+3}{2x^2$+1}.$$

Accepted Answer

$$y = \frac{5}{2}$$

Question 15

Find the horizontal asymptote of $$f(x) = \frac{4x^2$+1}{4x^2$+3}.$$

Accepted Answer

$$y = 1$$

Question 16

Which of the following could be the graph of $$f(x) = x^3$ - 4x^2$?

Accepted Answer

A cubic graph with $$x-$$intercepts at $$x = 0$$ and $$x = 4$$, and a local minimum between them.

Question 17

A chemical reaction rate is modeled by $$f(x) = \frac{3x+4}{2x+1}. If $$the rate must not exceed 2, what is the maximum value of $$x$$ allowed?

Accepted Answer

$$x \u003c 1$$

Question 18

A company’s profit is modeled by $$P(x) = -x^2$ + 6x - 4$$, where $$x is $$the number of units sold. What is the maximum profit and at how many units sold does it occur?

Accepted Answer

Maximum profit is $$5 at$$ $$x = 3$$ units.

Question 19

A medical dosage is modeled by $$f(x) = 5x + 8. If $$the maximum safe dosage is 33 mg, what is the maximum value of $$x$$ that can be administered?

Accepted Answer

$$x = 5$$

College Algebra Study Guide: Functions, Polynomials, and Rational Functions

Guida di studio - Domande di pratica

Study guide - Flashcard