Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^3$ - x + 7$$?

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

Question 1

Which of the following is the correct interval notation for the set of all real numbers $$x$$ such that $$x \u003e 2$$?

Accepted Answer

$$(2, \infty)$$

Question 2

Given the graph of a function that passes the vertical line test, which of the following statements is true?

Accepted Answer

The graph represents a function because each $$x-$$value corresponds to exactly one $$y-$$value.

Question 3

Suppose $$f(x) = 2x - 7. $$What is the $$x-$$intercept of the graph of $$f$$?

Accepted Answer

$$(3.5, 0)$$

Question 4

A car travels 368 miles using 16 gallons of gas and 115 miles using 5 gallons. What is the average rate of change in miles per gallon between these two points?

Accepted Answer

$$\frac{368 - 115}{16 - 5} = \frac{253}{11} \approx 23$$ miles/gallon

Question 5

Which of the following equations represents a vertical line?

Accepted Answer

$$x = 5$$

Question 6

If $$f(x) = |x - 3|$$, which of the following is the correct piecewise definition?

Accepted Answer

$$f(x) = x - 3$$ for $$x \geq 3$$, $$f(x) = 3 - x$$ for $$x \u003c 3$$

Question 7

Which of the following functions is even?

Accepted Answer

$$h(x) = x^2$

Question 8

Given $$f(x) = x^2$ + 3x$$ and $$g(x) = 2x - 1$$, what is $$(f + g)(-5)$$?

Accepted Answer

$$f(-5) + g(-5) = (25 - 15) + (-10 - 1) = 10 + (-11) = -1$$

Question 9

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^3$ - x + 7$$?

Accepted Answer

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

Question 10

If $$f(x) = \sqrt{x - 3} + 2$$, what is the domain of $$f$$?

Accepted Answer

$$[3, \infty)$$

Question 11

Which of the following is the correct formula for the average rate of change of $$f(x) on$$ $$[a, b]$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 12

Which of the following is the correct equation for a circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 13

If $$f(x) = 2x^2$ - 8x + 9$$, what are the coordinates of the vertex of the parabola?

Accepted Answer

$$(2, 1)$$

Question 14

Which of the following is the correct solution to $$|x - 4| = 7$$?

Accepted Answer

$$x = 11 or$$ $$x = -3$$

Question 15

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

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

Question 16

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(3) = 9$$

Question 17

Which of the following is the correct solution to the equation $$2x^2 = -48$?

Accepted Answer

$$x = \pm 4.9i$$

Precalculus Study Notes: Relations, Functions, and Linear Equations

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