Question 1

Given the function $f(x) = 2x^2 - 3x + 5$, what is the value of $f(-2)$?

Accepted Answer

$f(-2) = 17$

Question 2

Which of the following best describes the domain of the function $g(x) = \sqrt{x-4}$ in the context of a physics application where $x$ represents time in seconds?

Accepted Answer

$x \geq 4$

Question 3

If $h(x) = \dfrac{5}{x-1}$, evaluate $h(3)$ and interpret its meaning if $h(x)$ represents the concentration of a chemical after $x$ hours.

Accepted Answer

$h(3) = 2.5$, meaning the concentration is 2.5 units after 3 hours.

Question 4

Given the function $f(x) = -2x + 7$, what is the $y$-intercept?

Accepted Answer

$(0, 7)$

Question 5

A company models its profit with the function $P(x) = 50x - 200$, where $x$ is the number of products sold. What is the minimum number of products the company must sell to make a profit?

Accepted Answer

$x = 6$

Question 6

Which of the following is the equation of an exponential growth function?

Accepted Answer

$y = 2^x$

Question 7

A scientist records the decay of a radioactive substance using the function $N(t) = 100e^{-0.3t}$, where $t$ is in years. What is the initial amount of the substance?

Accepted Answer

$100$

Question 8

Which of the following is the correct graph for the exponential function $y = 3^x$?

Accepted Answer

A curve that increases rapidly for $x > 0$ and approaches zero as $x$ decreases.

Question 9

A hospital tracks the number of bacteria in a sample using $B(t) = 200 	imes 2^t$, where $t$ is in hours. How many bacteria will there be after 3 hours?

Accepted Answer

$1600$

Question 10

List all possible outcomes when tossing a coin and rolling a six-sided die.

Accepted Answer

$\{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6\}$

Question 11

How many different ways can a committee of 3 be chosen from 8 people?

Accepted Answer

$56$

Question 12

A bag contains 4 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is blue?

Accepted Answer

$\dfrac{1}{3}$

Question 13

If two events $A$ and $B$ are independent and $P(A) = 0.4$, $P(B) = 0.5$, what is $P(A \cap B)$?

Accepted Answer

$0.2$

Question 14

A card is drawn from a standard deck. What is the probability that it is a heart or a king?

Accepted Answer

$\dfrac{16}{52}$

Question 15

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

Accepted Answer

$7$

Question 16

A student flips two coins. What is the probability that both coins show heads?

Accepted Answer

$\dfrac{1}{4}$

Question 17

A box contains 5 light bulbs, 2 of which are defective. If two bulbs are selected at random without replacement, what is the probability that both are defective?

Accepted Answer

$\dfrac{1}{10}$

Question 18

If $P(A) = 0.3$, $P(B) = 0.5$, and $P(A \cap B) = 0.1$, what is $P(A \cup B)$?

Accepted Answer

$0.7$

Question 19

A password consists of 2 letters followed by 3 digits. How many different passwords are possible if letters and digits can be repeated?

Accepted Answer

$676,000$

Question 20

A medical test for a disease is 95% accurate. If 1% of the population has the disease, what is the probability that a randomly selected person tests positive (assuming the test never gives a false positive)?

Accepted Answer

$0.0095$

Functions and Probability: Key Concepts in College Algebra

Study Guide - Practice Questions

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