Q: Which of the following is the domain of the function $$f(x) = \\frac{1}{x-4}$$?

$$x \\in \\mathbb{R}, x \\neq 4$$

Question 1

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $$f(x) = x^2$ - 6$$, what is the value of $$f(-2)$$?

Accepted Answer

$$10$$

Question 3

Which of the following graphs represents a function?

Accepted Answer

A graph where no vertical line intersects the graph more than once.

Question 4

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

Accepted Answer

$$11$$

Question 5

A chemical reaction's rate $$R is $$modeled by $$R(t) = 5e$$^{-0.2t}$$, where t$ is time in minutes. What is the rate after 10$ minutes?

Accepted Answer

$$R(10) = 5e$$^{-2}$$

Question 6

Which of the following is the domain of the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$x \in \mathbb{R}, x \neq 4$$

Question 7

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 8

Which of the following is NOT a one-to-one function?

Accepted Answer

$$f(x) = x^2$

Question 9

If $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts of the function?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 10

A medical dosage $$D is $$given by $$D(w) = 0.1w + 5$$, where $$w is $$the patient's weight in kg. What is the dosage for a patient weighing $$70 kg$$?

Accepted Answer

$$D(70) = 12$$

Question 11

Which of the following describes the range of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$y \geq 0$$

Question 12

If $$f(x) = 3x - 2$$ and $$f^{-1}(x$$)$$ is the inverse, what is f$$^{-1}$$(7)$$?

Accepted Answer

$$3$$

Question 13

A car's value $$V$$ depreciates exponentially according to $$V(t) = 20000 \cdot (0.85)^t$$, where $$t is $$years after purchase. What is the value after $$3$$ years?

Accepted Answer

$$20000 \cdot (0.85)^3$

Question 14

Which of the following is the composition $$h(x) = f(g(x)) if$$ $$f(x) = x + 2$$ and $$g(x) = x^2$?

Accepted Answer

$$h(x) = x^2$ + 2$$

Question 15

Which of the following is the correct simplification of $$f(x) = \frac{x^2$ - 9}{x - 3}$$ for $$x \neq 3$$?

Accepted Answer

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

Question 16

A historical event occurred in year $$y. $$The number of years since the event is modeled by $$N(x) = x - y$$, where $$x is $$the current year. If the event was in $$1990$$ and the current year is $$2024$$, what is $$N(2024)$$?

Accepted Answer

$$34$$

Question 17

Which of the following is the correct domain for the function $$f(x) = \sqrt{5 - x}$$?

Accepted Answer

$$x \leq 5$$

Question 18

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

Accepted Answer

$$5$$

Question 19

A savings account earns interest according to $$A(t) = 1000 \cdot (1.03)^t$$, where $$t is $$years. What is the amount after $$5$$ years?

Accepted Answer

$$1000 \cdot (1.03)^5$

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