Question 1

Which of the following best describes a function $$f: X \rightarrow Y$$?

Accepted Answer

A rule that assigns each element in $$X to $$exactly one element in $$Y.$$

Question 2

Given the function $$I(t) = 100(0.06)t$$, what is the value of $$I$$ when $$t = 5$$?

Accepted Answer

$$I = 100(0.06)(5) = 30$$

Question 3

In the equation $$y = x + 2$$, which variable is the independent variable?

Accepted Answer

$$x$$

Question 4

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

Accepted Answer

$$y^2 = x$

Question 5

What is the domain of the function $$h(x) = \frac{1}{x-6}$$?

Accepted Answer

$$(-\infty, \infty) - \{6\}$$

Question 6

Which of the following is true about the equality of two functions $$f$$ and $$g$$?

Accepted Answer

They are equal if their domains are equal and $$f(x) = g(x)$$ for all $$x in $$the domain.

Question 7

Given $$f(x) = x^2$ + 5$$, what is the domain of $$f$$?

Accepted Answer

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

Question 8

Which of the following is a constant function?

Accepted Answer

$$h(x) = 2$$

Question 9

Which of the following is NOT a polynomial function?

Accepted Answer

$$g(x) = \sqrt{x}$$

Question 10

Which of the following is a rational function?

Accepted Answer

$$g(x) = \frac{2x+3}{x}$$

Question 11

Given the case-defined function $$F(s)$$:

$$F(s) = \begin{cases} 1 & 	ext{if } -1 \u003c s \u003c 1 \ 0 & 	ext{if } 1 \u003c s \u003c 2 \ s-3 & 	ext{if } 2 \u003c s \u003c 8 \end{cases}$$

What is $$F(7)$$?

Accepted Answer

$$4$$

Question 12

What is the domain of the absolute-value function $$f(x) = |x|$$?

Accepted Answer

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

Question 13

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

Accepted Answer

$$x^2 + x + 1$

Question 14

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

Accepted Answer

$$(x + 1)^2$

Question 15

Which of the following is the correct composite function $$(f \circ g)(x) if$$ $$f(x) = 2x - 1$$ and $$g(x) = x^2$?

Accepted Answer

$$2x^2 - 1$

Question 16

Which of the following is the degree of the polynomial $$f(x) = 6x^3$ + 7$$?

Accepted Answer

$$3$$

Question 17

Which of the following is the leading coefficient of $$f(x) = 3x^2$ - 8x + 9$$?

Accepted Answer

$$3$$

Question 18

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

Accepted Answer

$$x^2(x + 1$$)$$

Question 19

Which of the following is NOT a rational function?

Accepted Answer

$$g(x) = x^2$ + 1$$

Functions and Their Properties in College Algebra

스터디 가이드 - 연습 문제