Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-3}$$?

Accepted Answer

$$[3, \infty)$$

Question 2

Given the points $$A(2, -1)$$ and $$B(-4, 5)$$, what is the distance between them?

Accepted Answer

$$6\sqrt{2}$$

Question 3

Which of the following equations represents a vertical line?

Accepted Answer

$$x = -2$$

Question 4

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

Accepted Answer

$$2x^2 + 3$

Question 5

A circle has the equation $$(x-1)^2$$ + $$(y+2)^2 = 25$. What are the center and radius of the circle?

Accepted Answer

Center $$(1, -2)$$, radius $$5$$

Question 6

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 7

Given $$f(x) = |x|$$, which statement about its graph is true?

Accepted Answer

It is symmetric with respect to the y-axis.

Question 8

If a function passes the vertical line test but fails the horizontal line test, what can be concluded?

Accepted Answer

It is a function but does not have an inverse that is also a function.

Question 9

Which transformation will shift the graph of $$f(x) to $$the right by 4 units?

Accepted Answer

$$f(x - 4)$$

Question 10

Given the line $$3x - 4y = 12$$, what is the slope of any line perpendicular to it?

Accepted Answer

$$\frac{4}{3}$$

Question 11

If $$f(x) = x^2$ + 2x + 1$$, what is the simplified form of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h + 2$$

Question 12

A rectangular garden is to be enclosed with 200 feet of fencing. If one side has length $$x$$, what is the area $$A as a $$function of $$x$$?

Accepted Answer

$$A = x(100 - x)$$

Question 13

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

Accepted Answer

$$[0, \infty)$$

Question 14

If $$f(x) = 3x - 2$$ and $$g(x) = x + 4$$, what is $$(f + g)(x)$$?

Accepted Answer

$$4x + 2$$

Question 15

Which of the following is the standard form of the equation of a circle with center $$(h, k)$$ and radius $$r$$?

Accepted Answer

$$(x - h)^2$ + (y - k)^2$ = r^2$

Question 16

Given $$f(x) = x^3$, which statement is true?

Accepted Answer

The function is odd.

Question 17

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

Accepted Answer

$$(-\infty, \infty)$$

Question 18

Which of the following best describes the effect of multiplying a function $$f(x) by a $$constant $$c \u003e 1$$?

Accepted Answer

The graph is vertically stretched by a factor of $$c.$$

Question 19

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

Accepted Answer

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

Precalculus Chapter 1: Functions and Graphs - Structured Study Notes

Study Guide - Practice Questions