Q: A polynomial $$P(x)$$ has zeros at $$x = 0 ($$multiplicity 3) and $$x = 2 ($$multiplicity 2). Which statement best describes the end behavior of $$P(x)$$?

$$P(x) \to \infty as$$ $$x \to \infty$$ and $$P(x) \to -\infty as$$ $$x \to -\infty$$

Question 1

Given the function $$f(x) = \dfrac{1}{x-3}$$, which of the following correctly describes its domain in interval notation?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 2

Find the average rate of change of $$f(x) = x^2$ + 2x$$ from $$x = 1 to$$ $$x = 4.$$

Accepted Answer

$$7$$

Question 3

Given $$f(x) = 2x + 5$$, what is the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2$$

Question 4

A function $$g(x) is $$defined as follows:

$$g(x) = \begin{cases} 2x + 1 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}$$

What is the range of $$g(x)$$?

Accepted Answer

$$(-\infty, 1) \cup [0, \infty)$$

Question 5

Given the line passing through points $$(2, 5)$$ and $$(4, 9)$$, what is its equation in slope-intercept form?

Accepted Answer

$$y = 2x + 1$$

Question 6

Suppose the cost function for producing $$x$$ items is $$C(x) = 50x + 200$$ and the revenue function is $$R(x) = 70x. $$What is the breakeven point?

Accepted Answer

$$x = 20$$

Question 7

Given $$f(x) = (x-2)^2$ - 9$$, convert $$f(x) to $$general form $$ax^2 + bx + c$.

Accepted Answer

$$x^2 - 4x - 5$

Question 8

A quadratic function $$f(x) = x^2$ - 6x + 8 is $$given. What are its $$x-$$intercepts?

Accepted Answer

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

Question 9

Given the zeros $$x = -1 ($$multiplicity 2), $$x = 3 ($$multiplicity 1), which of the following is the polynomial of least degree?

Accepted Answer

$$f(x) = (x + 1)^2$(x - 3)$$

Question 10

A polynomial $$P(x)$$ has zeros at $$x = 0 ($$multiplicity 3) and $$x = 2 ($$multiplicity 2). Which statement best describes the end behavior of $$P(x)$$?

Accepted Answer

$$P(x) 	o \infty as$$ $$x 	o \infty$$ and $$P(x) 	o -\infty as$$ $$x 	o -\infty$$

Question 11

A piecewise function models a parking fee: $$f(x) = \begin{cases} 5 & 0 \leq x \leq 2 \ 5 + 2(x-2) & x \u003e 2 \end{cases}$$, where $$x is $$hours parked. What is the fee for 4 hours?

Accepted Answer

$$9$$

Question 12

Given $$f(x) = x^2$ and the transformation g(x) = f(x-3) + 2$, what is the vertex of g(x$$)$$?

Accepted Answer

$$(3, 2)$$

Precalculus Study Guide: Functions, Graphs, and Polynomial Analysis

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