Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $$f(x) = x^2$ + 1$$, what is the domain and range of $$f$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[1, \infty)$$

Question 3

Which of the following graphs passes the vertical line test and represents a function?

Accepted Answer

A parabola opening upwards.

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 rational function is undefined for which values?

Accepted Answer

Values that make the denominator zero.

Question 6

Which of the following is an even function?

Accepted Answer

$$f(x) = x^4$ - 2x^2$ + 1$$

Question 7

Which of the following is true for an odd function $$f(x)$$?

Accepted Answer

$$f(-x) = -f(x)$$ for all x in the domain.

Question 8

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

Accepted Answer

$$\{x \mid x 
eq 1\}$$

Question 9

A pizza chain finds that at a price of $$p = 14$$, $$d = 400$$ pizzas are sold per week, and at $$p = 17$$, $$d = 250. $$What is the demand function $$d(p)$$ assuming it is linear?

Accepted Answer

$$d(p) = -50p + 1100$$

Question 10

Which of the following is a piecewise function?

Accepted Answer

$$g(x) = \begin{cases} x, & x  2 \end{cases}$$

Question 11

What is the difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h} = 2x + h$$

Question 12

Which of the following is NOT a type of function discussed in the library of functions?

Accepted Answer

Hyperbolic tangent function

Question 13

If a graph is symmetric with respect to the y-axis, what can you conclude about the function?

Accepted Answer

It is an even function.

Question 14

Which of the following is the correct symbolic representation for the composition $$f(g(x))$$?

Accepted Answer

$$f(g(x))$$

Question 15

A function $$f is $$defined as $$f(x) = \sqrt{4 - x^2$}. $$What is the domain of $$f$$?

Accepted Answer

$$[-2, 2]$$

Question 16

Which of the following is a real-world example of a rational function?

Accepted Answer

The speed $$v of a $$car as a function of time $$t$$ given by $$v(t) = \frac{100}{t+2}$$

Question 17

If $$f(x) = x^3$ and g(x) = x + 1$, what is (f + g)(2$$)$$?

Accepted Answer

$$11$$

Question 18

Which of the following statements about the symmetry of functions is correct?

Accepted Answer

A function cannot be symmetric with respect to the x-axis.

Chapter 1: Functions – Foundations for Calculus

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