Question 1

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

Accepted Answer

$$[3, \infty)$$

Question 2

A circle has the equation $$(x-2)^2 + (y+5)^2 = 16.$$ What are the center and radius of the circle?

Accepted Answer

Center: $$(2, -5)$$, Radius: $$4$$

Question 3

Given the function $$f(x) = 2x^2$ - 5x + 3$$, find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$4x + 2h - 5$$

Question 4

Which of the following equations represents a vertical line?

Accepted Answer

$$x = -2$$

Question 5

A company’s cost function is $$C(x) = 15x + 200$$, where $$x is $$the number of units produced. What does the slope of this function represent in a real-world context?

Accepted Answer

The cost per unit produced

Question 6

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 7

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

Accepted Answer

$$3x^2 - 2$

Question 8

Which of the following best describes the transformation from $$f(x) = x^2$ to g(x$$) = $$2(x-3)^2 + 5$?

Accepted Answer

Shift right 3 units, stretch vertically by 2, shift up 5 units

Question 9

Given the points $$(1, 4)$$ and $$(5, 12)$$, what is the equation of the line passing through these points in slope-intercept form?

Accepted Answer

$$y = 2x + 2$$

Question 10

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 11

A function $$f is $$defined by $$f(x) = 2x + 1. $$What is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

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

Question 12

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

Accepted Answer

It is even and symmetric about the y-axis.

Question 13

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

Accepted Answer

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

Question 14

A rectangular garden is to be enclosed with 100 meters of fencing. Express the area $$A as a $$function of the width $$x.$$

Accepted Answer

$$A(x) = x(50 - x)$$

Question 15

Which of the following is the average rate of change of $$f(x) = x^3$ from x = 1$ to x = 3$?

Accepted Answer

$$14$$

Question 16

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

Accepted Answer

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

Question 17

Which of the following best describes the vertical line test?

Accepted Answer

A graph is a function if every vertical line intersects it at most once.

Question 18

Given $$f(x) = x^2$ - 4x + 7$$, what is the y-intercept of the graph of $$f$$?

Accepted Answer

$$7$$

Question 19

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

Accepted Answer

$$[0, \infty)$$

Precalculus Chapter 1: Functions and Graphs – Comprehensive Study Notes

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