Q: Which of the following best describes the domain of the function $$F(x) = \sqrt{2x+6} \div (x-2)$$?

$$\{x\mid x \geq -3, x \neq 2\}$$

Q: Given $$f(x) = \frac{1}{x-3}$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$(f-g)(x)$$?

$$\{x\mid x \geq 0, x \neq 3\}$$

Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4), (4,5)\}$$

Question 2

Given the function $$f(x) = 2x^2$ - 5$$, what is the value of $$f(3)$$?

Accepted Answer

$$3$$

Question 3

Which of the following best describes the domain of the function $$F(x) = \sqrt{2x+6} \div (x-2)$$?

Accepted Answer

$$\{x\mid x \geq -3, x 
eq 2\}$$

Question 4

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

Accepted Answer

$$7$$

Question 5

A relation is given by the set $$\{(1,4), (2,5), (3,6), (1,7)\}. Is $$this relation a function?

Accepted Answer

No, because the $$x$$ value 1 is paired with two different $$y$$ values.

Question 6

Given $$f(x) = x^2$ - 3x$$ and $$g(x) = 2x + 1$$, find $$(f \cdot g)(1).$$

Accepted Answer

$$-4$$

Question 7

Which of the following equations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$x = y^2$

Question 8

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

Accepted Answer

$$\{x\mid x 
eq 0\}$$

Question 9

A pharmaceutical company models the concentration $$C of a $$drug in the bloodstream as $$C(t) = \frac{50}{t+2}$$, where $$t is $$the time in hours after administration. What is the domain of $$C in $$this context?

Accepted Answer

$$\{t\mid t \geq 0\}$$

Question 10

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

Accepted Answer

$$\{x\mid x \geq 0\}$$

Question 11

Evaluate the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$f(x) = 3x + 2.$$

Accepted Answer

$$3$$

Question 12

Which of the following real-world scenarios is best modeled by a function?

Accepted Answer

Assigning each person in a city to their favorite color (people may have the same favorite color).

Question 13

Given $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$\{x\mid x \geq 1\}$$

Question 14

If $$f(x) = x^2$ and g(x) = x+1$, what is $$\left(\frac{f}{g}\right)(-1)$$?

Accepted Answer

$$0$$

Question 15

A cube's volume $$V is $$given as a function of its side length $$s by$$ $$V(s) = s^3$. What is the most appropriate domain for V$ in a real-world context?

Accepted Answer

$$\{s\mid s \u003e 0\}$$

Question 16

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

Accepted Answer

$$\{x\mid x \geq 0, x 
eq 3\}$$

Question 17

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

Accepted Answer

$$8$$

Question 18

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

Accepted Answer

$$2x + h$$

Question 19

A relation is given by the set $$\{(a,1), (b,2), (c,3), (a,4)\}. $$What is the domain of this relation?

Accepted Answer

$$\{a,b,c\}$$

Precalculus Study Notes: Functions and Their Graphs (Section 1.1)

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