Q: For the polynomial $$f(x) = x^4$ - 2x^2$ + 1$$, what is the end behavior of the graph?

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

Q: Given $$f(x) = \frac{3x}{x^2$ - 25}$$, what is the domain of $$f(x)$$?

$$x \in \mathbb{R}, x \neq 5, x \neq -5$$

Question 1

Which of the following is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 2

What is the result of $$(5 - 2i) + (3 + 3i)$$?

Accepted Answer

$$8 + i$$

Question 3

If $$z = 4 - 3i$$, what is the complex conjugate of $$z$$?

Accepted Answer

$$4 + 3i$$

Question 4

What is the product of $$(2 - i)(1 - i)$$?

Accepted Answer

$$3 - 3i$$

Question 5

Which of the following is the principal square root of $$-27$$?

Accepted Answer

$$3i\sqrt{3}$$

Question 6

Solve the quadratic equation $$x^2 + 2x + 5 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = -1 \pm 2i$$

Question 7

Given the quadratic function $$f(x) = -2(x - 3)^2$ + 5$$, what is the vertex of the parabola?

Accepted Answer

$$(3, 5)$$

Question 8

For the polynomial $$f(x) = x^4$ - 2x^2$ + 1$$, what is the end behavior of the graph?

Accepted Answer

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

Question 9

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = \sqrt{x} + 2x$$

Question 10

Find all possible rational zeros of $$f(x) = 2x^3$ - 5x^2$ + x - 6$$ using the Rational Zero Theorem.

Accepted Answer

$$\pm1, \pm2, \pm3, \pm6, \pm\frac{1}{2}, \pm\frac{3}{2}$$

Question 11

Given $$f(x) = \frac{3x}{x^2$ - 25}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 5, x 
eq -5$$

Question 12

For the rational function $$f(x) = \frac{x^2$ + 3x - 4}{x - 2}$$, what is the vertical asymptote?

Accepted Answer

$$x = 2$$

Question 13

What is the horizontal asymptote of $$f(x) = \frac{4x^2$ + 1}{2x^2$ - 3}$$?

Accepted Answer

$$y = 2$$

Question 14

A company manufactures wheelchairs with a fixed monthly cost of $$500,000 and a variable cost of 400$ per wheelchair. What is the average cost per wheelchair if 1000$ wheelchairs are produced in a month?

Accepted Answer

$$900$$

Question 15

Solve the inequality $$x^2 - x$$ \u003e 20$$.

Accepted Answer

$$x  5.12$$

Question 16

Given $$f(x) = x^3$ - 2x^2$ - 5x + 6$$, which of the following is a zero of $$f(x)$$?

Accepted Answer

$$x = -1$$

Question 17

Using Descartes’ Rule of Signs, how many possible positive real zeros does $$f(x) = x^4$ - 3x^3$ + 2x^2$ - x + 1$$ have?

Accepted Answer

2 or 0

Question 18

Which transformation shifts the graph of $$f(x) = \frac{1}{x}$$ two units to the left?

Accepted Answer

$$f(x) = \frac{1}{x + 2}$$

Question 19

If $$f(x) = x^4$ - 6x^3$ + 22x^2$ - 30x + 13$$, how many real roots does the equation have?

Accepted Answer

4

Precalculus Study Notes: Complex Numbers, Quadratic, Polynomial, and Rational Functions

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