Question 1

Which of the following points is located 3 units to the left of the origin and 2 units up in the rectangular coordinate system?

Accepted Answer

$$(-3, 2)$$

Question 2

Given the equation $$y = 2x + 1$$, what is the y-intercept of its graph?

Accepted Answer

$$(0, 1)$$

Question 3

Which of the following relations is NOT a function?

Accepted Answer

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

Question 4

If $$f(x) = x^2$ - 4$$, what is the range of $$f$$?

Accepted Answer

$$[-4, \infty)$$

Question 5

Which of the following equations represents a vertical line?

Accepted Answer

$$x = 5$$

Question 6

A function $$f is $$defined as $$f(x) = |x|. $$Which of the following statements is true?

Accepted Answer

The function is even and symmetric about the y-axis.

Question 7

Given the points $$(2, 3)$$ and $$(6, 11)$$, what is the slope of the line passing through them?

Accepted Answer

$$2$$

Question 8

Which transformation describes the graph of $$g(x) = f(x - 4) + 2$$ compared to $$f(x)$$?

Accepted Answer

Shift right 4 units and up 2 units

Question 9

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

Accepted Answer

$$f(g(2)) = 3 \cdot 4 - 1 = 11$$

Question 10

Which of the following functions has an inverse that is also a function?

Accepted Answer

$$f(x) = x^3$

Question 11

What is the standard form of the equation of a circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

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

Question 12

A line passes through $$(1, 2)$$ and is perpendicular to the line $$y = -\frac{1}{2}x + 3. $$What is the slope of the new line?

Accepted Answer

$$2$$

Question 13

Given $$f(x) = x^2$ + 1$$ and $$g(x) = x - 3$$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$x 
eq 3$$

Question 14

If the cost to frame a degree at Shop A is $$f(x) = 20 + 10x$$ and at Shop B is $$g(x) = 25 + 8.75x$$, for what value of $$x do $$the costs equal each other?

Accepted Answer

$$x = 4$$

Question 15

Which of the following best describes the average rate of change of $$f(x) = 2x^2$ from x = 1$ to x = 4$?

Accepted Answer

$$\frac{f(4) - f(1)}{4 - 1} = \frac{32 - 2}{3} = 10$$

Question 16

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h} = \frac{(x+h)^2$ - x^2$}{h}$$

Question 17

A function $$f is $$defined as $$f(x) = \sqrt{x-2}. $$What is the domain of $$f$$?

Accepted Answer

$$x \geq 2$$

Question 18

If $$f(x) = 2x + 1$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

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

Question 19

What is the distance between the points $$(1, 2)$$ and $$(4, 6)$$?

Accepted Answer

$$5$$

Precalculus Chapter 1: Functions and Graphs - Structured Study Notes

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