Question 1

Which of the following relations is a function?

Accepted Answer

The relation $$\{(1, 4), (2, 5), (3, 6)\}$$

Question 2

Which graph passes the vertical line test and therefore represents a function?

Accepted Answer

A graph with a sharp turn and a jump discontinuity

Question 3

Given the piecewise function $$f(x) = \begin{cases} 4 & x \u003c 3 \ x^2$ - 3 & 3 \leq x \u003c 8 \ x^2$ & x \geq 8 \end{cases}$$, what is $$f(-1)$$?

Accepted Answer

$$f(-1) = 4$$

Question 4

What is the domain of the function $$f(x) = x^2$ + 5$$?

Accepted Answer

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

Question 5

Which interval notation correctly expresses the range of the graph shown if its lowest point is $$y = -2$$ and its highest point is $$y = 5$$?

Accepted Answer

$$[-2, 5]$$

Question 6

A piecewise function is defined as $$f(x) = \begin{cases} x+1 & x \leq 2 \ x^2$ + 5 & x \u003e 2 \end{cases}. $$What is $$f(2)$$?

Accepted Answer

$$f(2) = 2 + 1 = 3$$

Question 7

Which of the following best describes the range of a function?

Accepted Answer

The set of all possible output values

Question 8

Given the piecewise function $$f(x) = \begin{cases} 2x + 4 & x \u003c 0 \ x^2$ & 0 \leq x \u003c 2 \ x^2$ + 5 & x \geq 2 \end{cases}$$, what is $$f(5)$$?

Accepted Answer

$$f(5) = 5^2$ + 5 = 30$$

Question 9

If a graph contains the points $$(-3, 5)$$, $$(0, 2)$$, and $$(3, 5)$$, is it a function?

Accepted Answer

Yes, because each input has only one output

Question 10

Which of the following is NOT a function?

Accepted Answer

A graph that fails the vertical line test

Question 11

For the piecewise function $$f(x) = \begin{cases} -4 & x \u003c -2 \ x + 1 & -2 \leq x \u003c 1 \ x^2$ & x \geq 1 \end{cases}$$, what is $$f(0)$$?

Accepted Answer

$$f(0) = 0 + 1 = 1$$

Question 12

Which of the following statements about piecewise functions is TRUE?

Accepted Answer

Piecewise functions can have jumps where the pieces do not match at endpoints

Question 13

If the domain of a function is $$[-4, 5)$$, which of the following is TRUE?

Accepted Answer

The function is defined for all $$x$$ such that $$-4 \leq x \u003c 5$$

Question 14

A business models its profit with the piecewise function $$P(x) = \begin{cases} 0 & x \u003c 0 \ 5x & 0 \leq x \u003c 100 \ 500 & x \geq 100 \end{cases}$$, where $$x is $$the number of units sold. What is the profit if 120 units are sold?

Accepted Answer

$$P(120) = 500$$

Question 15

Which of the following is the correct set builder notation for the range $$[-1, 2)$$?

Accepted Answer

$$\{y \mid -1 \leq y \u003c 2\}$$

Question 16

A function $$f is $$defined by $$f(x) = x^2$ for x$$ \in [-2, 3]$$. What is the range of f$?

Accepted Answer

$$[0, 9]$$

Question 17

Which of the following is a correct way to combine two functions $$f(x)$$ and $$g(x)$$?

Accepted Answer

$$f(x) + g(x)$$

Question 18

If a graph has multiple intervals in its domain, how is this expressed in interval notation?

Accepted Answer

By using the union symbol $$\cup$$

Question 19

Which of the following is the correct interval notation for all real numbers except $$x = 2$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Relations, Functions, Domain & Range, and Piecewise Functions: Business Calculus Study Notes

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