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 $$x \u003e 0$$ 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

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