Q: Given $$f(x) = x^4$ - 2x^2$ + 1$$, which of the following describes the end behavior of $$f(x)$$?

As $$x \to \pm\infty$$, $$f(x) \to \infty$$

Question 1

Given the function $$f(x) = x^3$ - 6x^2$ + 9x$$, which of the following intervals is where the function is decreasing?

Accepted Answer

$$(0, 3)$$

Question 2

Suppose the graph of $$f(x) is $$reflected over the $$y-$$axis and shifted up 2 units. Which equation represents the new function?

Accepted Answer

$$f(-x) + 2$$

Question 3

Find the domain of the function $$f(x) = \dfrac{2x}{x^2$ - 9}.$$

Accepted Answer

$$x 
eq \pm 3$$

Question 4

A ball is thrown vertically upward from the top of a building 800 feet tall with an initial velocity of 80 feet per second. The distance $$d (in $$feet) of the ball from the ground after $$t$$ seconds is given by $$d(t) = -16t^2$ + 80t + 800. $$What is the maximum height of the ball?

Accepted Answer

$$1000$$ feet

Question 5

Given $$f(x) = x^4$ - 2x^2$ + 1$$, which of the following describes the end behavior of $$f(x)$$?

Accepted Answer

As $$x 	o \pm\infty$$, $$f(x) 	o \infty$$

Question 6

Which of the following is the sum of $$f(x) = x^2$ - 9x$$ and $$g(x) = 2x + 3$$?

Accepted Answer

$$x^2 - 7x + 3$

Question 7

A radioactive substance decays according to the model $$A(t) = Ae$$^{-0.07t}$$, where A$ is the initial amount present and t$ is time in years. After 12 years, what percent of the original amount remains?

Accepted Answer

$$43\%$$

Question 8

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - 2x$$

Question 9

Given $$f(x) = x^2$ - 4x + 3$$, find the $$x-$$intercepts of the function.

Accepted Answer

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

Question 10

Which of the following is the correct expression for $$\log(x^2$ - 9) - \log(x - 3) as a $$single logarithm?

Accepted Answer

$$\log\left(\dfrac{x^2$ - 9}{x - 3}\right)$$

Question 11

A company charges a fixed cost of $$1500$$ with a variable cost per unit of $$22. $$The commodity is sold for $$50$$ per unit. Which equation models the profit $$P$$ for $$x$$ units sold?

Accepted Answer

$$P = 50x - 22x - 1500$$

Question 12

Find the solution to the system of equations: $$\begin{cases} 2x + 3y = 12 \ x - y = 2 \end{cases}$$

Accepted Answer

$$x = 4, y = 2$$

Question 13

Suppose $$f(x) = \sqrt{x - 2}. $$What is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 2$$

Question 14

Which of the following is the correct solution to $$4^x = 64$$?

Accepted Answer

$$x = 3$$

Question 15

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

Accepted Answer

$$(2x + 3)^2$

Question 16

A large group of students is asked to memorize a list of 60 Italian words. The number of words retained is modeled by $$W(t) = 60e$$^{-0.2t}$$, where t$ is the number of hours after memorization. How many words are remembered after 5 hours?

Accepted Answer

$$22$$

Question 17

Which of the following is the correct expression for the difference quotient of $$f(x) = x^2$?

Accepted Answer

$$\dfrac{f(x+h) - f(x)}{h} = \dfrac{(x+h)^2$ - x^2$}{h}$$

Question 18

Which of the following is the correct solution to $$6e^x = 9$$?

Accepted Answer

$$x = \ln(1.5)$$

Question 19

Given $$f(x) = x^2$ - 4$$, which of the following is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt{x + 4}$$ and f$$^{-1}$$(x) = -\sqrt{x + 4}$$

College Algebra Final Exam Review: Comprehensive Study Notes

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