Q: Given the piecewise function $f(x) = \begin{cases} x, & x < 0 \\ 2, & 0 \leq x < 1 \\ 1, & x \geq 1 \end{cases}$, which of the following statements is true?

The function is discontinuous at $x = 0$ and $x = 1$.

Q: For the function $f(x) = |x-2| - 1$, which transformation has been applied to the parent function $y = |x|$?

Shift right by 2 units and down by 1 unit.

Q: For the function $f(x) = \frac{1}{1-e^x}$, what is its domain?

$(-\infty, 0) \cup (0, \infty)$

Q: Which of the following is the correct application of the Intermediate Value Theorem?

If $f$ is continuous on $[a, b]$ and $f(a) 0$, then there exists $c \in (a, b)$ such that $f(c) = 0$.

Question 1

Which of the following is the domain of the function $f(x) = \frac{2x+1}{x^2-x-2}$?

Accepted Answer

$(-\infty, -1) \cup (-1, 2) \cup (2, \infty)$

Question 2

Given the piecewise function $f(x) = \begin{cases} x, & x < 0 \ 2, & 0 \leq x < 1 \ 1, & x \geq 1 \end{cases}$, which of the following statements is true?

Accepted Answer

The function is discontinuous at $x = 0$ and $x = 1$.

Question 3

Which of the following functions is odd?

Accepted Answer

$f(x) = x^3 + x$

Question 4

For the function $f(x) = |x-2| - 1$, which transformation has been applied to the parent function $y = |x|$?

Accepted Answer

Shift right by 2 units and down by 1 unit.

Question 5

Which of the following is the correct composite function for $f(x) = \sqrt{x}$ and $g(x) = x^2 + 1$?

Accepted Answer

$f(g(x)) = \sqrt{x^2 + 1}$

Question 6

Which of the following is the period of the function $f(x) = 	an x$?

Accepted Answer

$\pi$

Question 7

If $\cos x = \frac{5}{13}$ and $x$ is in the fourth quadrant, what is $\sin x$?

Accepted Answer

$-\frac{12}{13}$

Question 8

Which of the following is a property of logarithms?

Accepted Answer

$\ln(ab) = \ln a + \ln b$

Question 9

Evaluate $\lim_{x 	o 0} \frac{\sin x}{x}$.

Accepted Answer

$1$

Question 10

Which of the following is the horizontal asymptote of $f(x) = \frac{x^2 - 1}{x^2 + 1}$?

Accepted Answer

$y = 1$

Question 11

Given $f(x) = 3x + 4$, $g(x) = 2x - 1$, express $f(g(x))$.

Accepted Answer

$6x + 1$

Question 12

Which of the following is true about the function $f(x) = x^2$?

Accepted Answer

It is an even function.

Question 13

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

Accepted Answer

$(-\infty, \infty)$

Question 14

Which of the following is the correct simplification for $\ln(8x+4) - 2\ln2$?

Accepted Answer

$\ln(2x+1)$

Question 15

For the function $f(x) = \frac{1}{1-e^x}$, what is its domain?

Accepted Answer

$(-\infty, 0) \cup (0, \infty)$

Question 16

Which of the following is the correct inverse of $f(x) = \frac{1}{2}x + 1$?

Accepted Answer

$f^{-1}(x) = 2x - 2$

Question 17

Which of the following is the correct application of the Intermediate Value Theorem?

Accepted Answer

If $f$ is continuous on $[a, b]$ and $f(a) < 0$, $f(b) > 0$, then there exists $c \in (a, b)$ such that $f(c) = 0$.

Question 18

Evaluate $\lim_{x 	o \infty} \frac{2x^2 + 5x + 1}{x^2 + 3}$.

Accepted Answer

$2$

Question 19

Which of the following is the correct result for $\lim_{x 	o 0} \frac{1 - \cos x}{\sin 2x}$?

Accepted Answer

$0$

Calculus Chapter 1: Functions, Limits, and Continuity – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards