Q: Given the table of U.S. household expenditures, which ordered pair correctly represents the relationship between the 'entertainment' category and the amount spent?

$$(\text{entertainment}, 3203)$$

Q: A function $$f is $$called even if:

$$f(-x) = f(x)$$ \text{ for all } x$

Question 1

Given the table of U.S. household expenditures, which ordered pair correctly represents the relationship between the 'entertainment' category and the amount spent?

Accepted Answer

$$(	ext{entertainment}, 3203)$$

Question 2

Which of the following best describes the coordinates of the midpoint between the points $$(8, -4)$$ and $$(-6, 1)$$?

Accepted Answer

$$\left(1, -1.5\right)$$

Question 3

The distance between the points $$P(-8, 4)$$ and $$Q(3, -2) is$$:

Accepted Answer

$$\sqrt{(3 - (-8))^2$ + ((-2) - 4)^2$} = \sqrt{11^2$ + (-6)^2$} = \sqrt{121 + 36} = \sqrt{157}$$

Question 4

Which of the following equations represents a circle with center $$(2, -5)$$ and radius $$7$$?

Accepted Answer

$$(x - 2)^2$ + (y + 5)^2$ = 49$$

Question 5

Given the relation $$\{(3, 1), (4, 2), (4, 5), (6, 8)\}$$, what is the domain?

Accepted Answer

Question 6

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1, 2), (2, 3), (1, 4)\}$$

Question 7

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

Accepted Answer

$$f(3) + g(3) = 9 + 7 = 16$$

Question 8

Which of the following best describes the range of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 9

A function $$f is $$called even if:

Accepted Answer

$$f(-x) = f(x)$$ 	ext{ for all } x$

Question 10

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

Accepted Answer

$$f(g(2)) = f(4) = 2 \cdot 4 - 1 = 7$$

Question 11

Which of the following statements about the graph of $$y = |x| is $$true?

Accepted Answer

$$y = |x|$$ decreases on $$(-\infty, 0)$$ and increases on $$(0, \infty)$$

Question 12

If $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of (f$$ \div g)(x)$$?

Accepted Answer

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

Question 13

Which transformation results in the graph of $$y = f(x) + 3$$ compared to $$y = f(x)$$?

Accepted Answer

A vertical shift upward by 3 units

Question 14

Given the function $$f(x) = x^2$ - 4x + 7$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h - 4$$

Question 15

Which of the following best describes the graph of $$y = f(-x)$$ compared to $$y = f(x)$$?

Accepted Answer

It is a reflection across the $$y-$$axis

Question 16

If the graph of a function passes the vertical line test, what does this indicate?

Accepted Answer

The relation is a function

Question 17

Given the general form of a circle $$x^2$$ + $$y^2 + Dx + Ey + F = 0$, what must be true for the graph to represent a real circle?

Accepted Answer

$$D^2$$ + $$E^2 - 4F$$ \u003e 0$$

Question 18

Which of the following is the correct composition $$(g \circ f)(x) if$$ $$f(x) = x + 2$$ and $$g(x) = x^2$?

Accepted Answer

$$(g \circ f)(x) = (x + 2)^2$

Question 19

If a function is defined as $$f(x) = |x|$$, which of the following statements is true?

Accepted Answer

$$f(x) is $$even

Graphs, Functions, and Coordinate Systems: Precalculus Study Notes

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