Q: A function $$f is $$odd if:

$$f(-x) = -f(x)$$ \text{ for all } x$

Question 1

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

Accepted Answer

$$x \geq 2$$

Question 2

Given the function $$f(x) = \dfrac{2x+1}{x-3}$$, which value is NOT in the domain of $$f$$?

Accepted Answer

$$x = 3$$

Question 3

A graph passes the vertical line test if and only if:

Accepted Answer

Every vertical line intersects the graph at most once.

Question 4

Let $$f(x) = x^2$ and g(x) = x+1$. What is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 5

Which of the following functions is even?

Accepted Answer

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

Question 6

Suppose $$h(x) = \ln(x^2$ - 1). $$What is the domain of $$h$$?

Accepted Answer

$$x  1$$

Question 7

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

Accepted Answer

$$\dfrac{(x+h)^2$ - x^2$}{h}$$

Question 8

A function $$f is $$odd if:

Accepted Answer

$$f(-x) = -f(x)$$ 	ext{ for all } x$

Question 9

Which of the following is a transcendental function?

Accepted Answer

$$f(x) = \sin(x)$$

Question 10

If $$f(x) = 3x^2$ - x$$ and $$g(x) = \dfrac{1}{x}$$, what is $$f(g(x))$$?

Accepted Answer

$$\dfrac{3}{x^2$} - \dfrac{1}{x}$$

Question 11

Which of the following best describes the range of the exponential function $$f(x) = 2^x$$?

Accepted Answer

$$f(x) \u003e 0$$

Question 12

Given the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ -x+2 & x \geq 0 \end{cases}$$, what is $$f(-3) + f(3)$$?

Accepted Answer

$$4$$

Question 13

Which of the following is the general form of a polynomial of degree $$n$$?

Accepted Answer

$$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_1$ x + a_0$

Question 14

A real-world example: The height $$h (in $$meters) of a ball thrown upward from the ground is given by $$h(t) = -4.9t^2$ + 20t. $$What is the maximum height reached by the ball?

Accepted Answer

$$20.41$$ meters

Question 15

Which of the following statements about the function $$f(x) = |x| is $$true?

Accepted Answer

It is even and its graph is symmetric about the y-axis.

Question 16

Given $$f(x) = x^3$ and a = 2$, what is the value of the difference quotient $$\dfrac{f(x) - f(a)}{x - a}$$?

Accepted Answer

$$x^2 + 2x + 4$

Question 17

Which of the following is NOT a property of an odd function?

Accepted Answer

The graph is symmetric about the y-axis.

Question 18

Which of the following is the correct formula for the slope of the secant line between points $$P(a, f(a))$$ and $$Q(x, f(x)) on $$the curve $$y = f(x)$$?

Accepted Answer

$$\dfrac{f(x) - f(a)}{x - a}$$

Question 19

Which of the following best describes the range of the logarithmic function $$f(x) = \log_b(x)$$, $$b \u003e 1$$?

Accepted Answer

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

Question 20

Suppose $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$. What is the domain of the composite function (g$$ \circ f)(x)$$?

Accepted Answer

$$x \in \mathbb{R} ($$all real numbers)

Chapter 1: Functions – Calculus Study Notes

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