Q: A function is defined as $f(x) = 3 - x^2$. Which transformation has been applied to the basic squaring function to obtain this function?

Reflected across the x-axis and shifted up 3 units

Q: Which of the following real-world scenarios can be modeled by a piecewise function?

A taxi fare that charges a flat rate for the first mile and a different rate for each additional mile

Q: Which of the following best describes the graph of $y = \lfloor x \rfloor$?

A step function with jumps at every integer

Question 1

Which of the following is the correct formula for the distance between Kiara and Matias after $t$ hours, if Kiara drives east at 35 mph and Matias drives north at 40 mph, starting from the same point?

Accepted Answer

$d(t) = \sqrt{(35t)^2 + (40t)^2}$

Question 2

Which of the following is the graph of the basic squaring function?

Accepted Answer

$y = x^2$

Question 3

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

Question 4

Which of the following best describes the transformation from the basic square root function $y = \sqrt{x}$ to $f(x) = \sqrt{x+3}$?

Accepted Answer

Shifted 3 units to the left

Question 5

What is the domain of the function $d(t) = \sqrt{(35t)^2 + (40t)^2}$, where $t$ represents time in hours?

Accepted Answer

$t \geq 0$

Question 6

Which of the following is the greatest integer less than or equal to $-2.7$?

Accepted Answer

$-3$

Question 7

Given the piecewise function $g(x) = \begin{cases} \frac{1}{3}x + 3 & x < 3 \ -x & x \geq 3 \end{cases}$, what is $g(4)$?

Accepted Answer

$-4$

Question 8

Which of the following is the correct graph for the absolute value function?

Accepted Answer

$y = |x|$

Question 9

A function is defined as $f(x) = 3 - x^2$. Which transformation has been applied to the basic squaring function to obtain this function?

Accepted Answer

Reflected across the x-axis and shifted up 3 units

Question 10

Evaluate the greatest integer function $f(x) = \lfloor x \rfloor$ at $x = 2.99$.

Accepted Answer

$2$

Question 11

Which of the following is NOT a basic function from the library of functions?

Accepted Answer

$y = \sin(x)$

Question 12

Given the piecewise function $h(x) = \begin{cases} 2x - 1 & x < 1 \ x^2 & x \geq 1 \end{cases}$, what is $h(1)$?

Accepted Answer

$2$

Question 13

Which of the following real-world scenarios can be modeled by a piecewise function?

Accepted Answer

A taxi fare that charges a flat rate for the first mile and a different rate for each additional mile

Question 14

If $f(x) = \sqrt{x+3}$, what is the domain of $f$?

Accepted Answer

$x \geq -3$

Question 15

Which of the following is the correct formula for the reciprocal function?

Accepted Answer

$y = \frac{1}{x}$

Question 16

Evaluate the piecewise function $f(x) = \begin{cases} x+2 & x < 0 \ x^2 & x \geq 0 \end{cases}$ at $x = 2$.

Accepted Answer

$4$

Question 17

Which of the following best describes the graph of $y = \lfloor x \rfloor$?

Accepted Answer

A step function with jumps at every integer

Question 18

If $f(x) = |x|$, which of the following statements is true?

Accepted Answer

$f(x)$ is always nonnegative

Question 19

Which of the following is the correct formula for the cube root function?

Accepted Answer

$y = \sqrt[3]{x}$

Chapter 2: More on Functions – College Algebra Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards