Question 1

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

Accepted Answer

$x \geq 2$

Question 2

Given the function $f(x) = x^2$, which transformation results in the graph of $f(x-3) + 2$?

Accepted Answer

Shift right by 3 units and up by 2 units

Question 3

Which of the following is the inverse function of $f(x) = 2x + 5$?

Accepted Answer

$f^{-1}(x) = \frac{x-5}{2}$

Question 4

If $f(x) = x^3$ and $g(x) = \sqrt{x}$, what is $(f \circ g)(x)$?

Accepted Answer

$(f \circ g)(x) = (\sqrt{x})^3$

Question 5

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

Accepted Answer

$(0, \infty)$

Question 6

A population of bacteria doubles every hour. If the initial population is $P_0$, which function models the population after $t$ hours?

Accepted Answer

$P(t) = P_0 \cdot 2^t$

Question 7

Which of the following is the correct summation notation for the sum $1 + 2 + 3 + \ldots + n$?

Accepted Answer

$\sum\limits_{k=1}^{n} k$

Question 8

Given $f(x) = x^2$ and $g(x) = x + 1$, what is the difference function $h(x) = f(x) - g(x)$?

Accepted Answer

$h(x) = x^2 - x - 1$

Question 9

Which of the following is the correct formula for the sum of the first $n$ terms of an arithmetic sequence with first term $a_1$ and common difference $d$?

Accepted Answer

$S_n = \frac{n}{2} [2a_1 + (n-1)d]$

Question 10

Which property of functions states that $f(-x)$ reflects the graph of $f(x)$ over the $y$-axis?

Accepted Answer

Even/Odd symmetry

Question 11

If $f(x) = \frac{1}{x}$, which of the following describes its graph?

Accepted Answer

It has a vertical asymptote at $x=0$ and a horizontal asymptote at $y=0$

Question 12

Which of the following is the correct formula for the sum of the first $n$ terms of a geometric sequence with first term $a_1$ and common ratio $r 
eq 1$?

Accepted Answer

$S_n = a_1 \frac{1 - r^n}{1 - r}$

Question 13

Which function is always increasing for all real $x$?

Accepted Answer

$f(x) = e^x$

Question 14

If $f(x) = x^2$ is an even function, which of the following is true?

Accepted Answer

$f(-x) = f(x)$

Question 15

Which of the following is the correct expression for the logarithmic function with base $a$?

Accepted Answer

$f(x) = \log_a(x)$

Question 16

A radioactive substance decays according to $N(t) = N_0 e^{-kt}$. What does $k$ represent?

Accepted Answer

Decay constant

Question 17

Which of the following is the correct formula for the $n$th term of an arithmetic sequence?

Accepted Answer

$a_n = a_1 + (n-1)d$

Question 18

If $f(x) = x^3$ and $g(x) = 2x$, what is the composition $(g \circ f)(x)$?

Accepted Answer

$(g \circ f)(x) = 2x^3$

Question 19

Which of the following is true about the function $f(x) = \ln(x)$?

Accepted Answer

Its domain is $(0, \infty)$

Foundations of Functions and Sequences in Calculus I

Study Guide - Practice Questions

Study Guide - Flashcards