Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 5}$$?

Accepted Answer

$$x \geq 2.5$$

Question 2

A company models its profit $$P (in $$thousands of dollars) as a function of time $$t (in $$years) by $$P(t) = 3t^2$ - 12t + 20. $$What is the minimum profit, and after how many years does it occur?

Accepted Answer

Minimum profit is $$2$$ thousand dollars at $$t = 2$$ years.

Question 3

Given the function $$f(x) = \dfrac{2x+1}{x-3}$$, which of the following describes its vertical asymptote?

Accepted Answer

$$x = 3$$

Question 4

If $$f(x) = x^2$ - 4x + 7$$ and $$g(x) = 2x - 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(2x-1)^2 - 4(2x-1) + 7$

Question 5

A bacteria population doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 500 \cdot 2$$^{t/3}$$

Question 6

Which of the following is the inverse function of $$f(x) = 5x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x + 7}{5}$$

Question 7

A projectile is launched from a cliff 80 meters high with an initial velocity of 20 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 80. $$After how many seconds does it reach its maximum height?

Accepted Answer

$$t = 2.04$$ seconds

Question 8

Which of the following is the solution set for $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 9

Given $$f(x) = x^2$ and g(x) = x + 3$, which of the following is f(g(x$$))$$?

Accepted Answer

$$(x + 3)^2$

Question 10

A car depreciates in value by 15% each year. If the car is currently worth $20,000, what will its value be after 4 years?

Accepted Answer

$$20,000 	imes (0.85)^4$

Question 11

Which of the following describes the range of the function $$f(x) = \dfrac{1}{x-2}$$?

Accepted Answer

$$y 
eq 0$$

Question 12

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

Accepted Answer

$$f^{-1}(7$$) = \dfrac{7 + 1}{3} = \dfrac{8}{3}$$

Question 13

Which of the following is the solution to the equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 14

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.2t}$$, where A_0$ is the initial amount. What is the half-life of the substance?

Accepted Answer

$$t = \dfrac{\ln 2}{0.2}$$

Question 15

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 16

If $$f(x) = \dfrac{1}{x}$$ and $$g(x) = x + 2$$, what is $$(f \circ g)(3)$$?

Accepted Answer

$$\dfrac{1}{5}$$

Question 17

A population grows according to $$P(t) = 1000e$$^{0.05t}$$. How long will it take for the population to double?

Accepted Answer

$$t = \dfrac{\ln 2}{0.05}$$

Question 18

Which of the following is the solution to the equation $$\log_3$(x) = 4$$?

Accepted Answer

$$x = 81$$

Question 19

If $$f(x) = x^2$ - 6x + 8$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 2 or$$ $$x = 4$$

Precalculus Homework Assignment 1 – Step-by-Step Study Guidance

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