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

$$\displaystyle \{x \mid x \neq 4\}$$

Question 1

Which of the following best describes the difference between an expression and an equation in algebra?

Accepted Answer

An expression contains variables and numbers connected by operations, while an equation states that two expressions are equal.

Question 2

A cell phone company offers two plans: Plan A charges \$$40 per month for unlimited calls, and Plan B charges \20 $$per month plus \$0.10 per minute. For how many minutes of calls per month will the two plans cost the same?

Accepted Answer

$$\displaystyle 200$$

Question 3

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

Accepted Answer

$$\displaystyle 21$$

Question 4

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

Accepted Answer

$$\displaystyle \{x \mid x 
eq 4\}$$

Question 5

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

Accepted Answer

$$\displaystyle 9$$

Question 6

A company models its revenue with the function $$R(t) = 5000e$$^{0.03t}$$, where t$ is the number of years since 2020. What is the revenue in 2025, rounded to the nearest dollar?

Accepted Answer

$$\displaystyle 5792$$

Question 7

Which of the following describes the graph of $$y = (x-2)^2$ + 3$$ compared to $$y = x^2$?

Accepted Answer

Shifted right 2 units and up 3 units

Question 8

Solve the inequality $$2x - 5 \u003e 7.$$

Accepted Answer

$$\displaystyle x \u003e 6$$

Question 9

Which of the following is the inverse function of $$f(x) = 3x - 4$$?

Accepted Answer

$$\displaystyle f$$^{-1}$$(x) = \dfrac{x+4}{3}$$

Question 10

A bacteria population doubles every 4 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$\displaystyle P = 500 \cdot 2$$^{t/4}$$

Question 11

Which of the following is the solution set for the quadratic equation $$x^2 - 6x + 5 = 0$?

Accepted Answer

$$\displaystyle \{1, 5\}$$

Question 12

Given $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$\displaystyle \{x \mid x \geq 1\}$$

Question 13

If $$f(x) = x^2$ and g(x) = 2x + 1$, find the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$.

Accepted Answer

$$\displaystyle 2x + h$$

Question 14

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$\displaystyle x = 32$$

Question 15

A circle has center at $$(2, -3)$$ and radius $$5. $$Which is its equation?

Accepted Answer

$$\displaystyle (x-2)^2$ + (y+3)^2$ = 25$$

Question 16

Solve the system of equations: $$\begin{cases} x + y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$\displaystyle x = 4,\ y = 3$$

Question 17

Which of the following is a one-to-one function?

Accepted Answer

$$\displaystyle f(x) = 2x + 1$$

Question 18

A car's value depreciates according to $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 3 years, rounded to the nearest dollar?

Accepted Answer

$$\displaystyle 12283$$

Question 19

Which of the following is the correct solution to the inequality $$\dfrac{x-2}{x+1} \u003e 0$$?

Accepted Answer

$$\displaystyle (-\infty, -1) \cup (2, \infty)$$

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