Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following best describes the purpose of function notation in algebra?

Accepted Answer

To represent the relationship between two variables using a specific rule or formula, such as $$f(x) = 2x + 3$$

Question 2

A student is given the quadratic equation $$x^2 - 6x + 8 = 0$. Which method would be most appropriate to solve for x$?

Accepted Answer

Factoring the quadratic equation

Question 3

Which of the following is the correct way to express the inverse of the function $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+5}{3}$$

Question 4

A real-world scenario: A company’s profit $$P (in $$thousands of dollars) is modeled by the function $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in hundreds). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$P(3) = 2$$ thousand dollars, at $$x = 3 (300 $$units)

Question 5

Which of the following statements about the graph of $$y = \frac{1}{x-2} is $$correct?

Accepted Answer

It has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 0$$

Question 6

Given the exponential equation $$5^{2x} = 125$, what is the value of x$?

Accepted Answer

$$x = 1.5$$

Question 7

A student is asked to solve the system of equations: $$\begin{cases} 2x + 3y = 12 \ x - y = 1 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

$$(3, 2)$$

Question 8

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

Accepted Answer

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

Question 9

If $$f(x) = 2x^2$ - 3x + 1$$ and $$g(x) = x - 4$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(-2) = 2(-2)^2$ - 3(-2) + 1 = 8 + 6 + 1 = 15$$

Question 10

Which of the following best describes the solution set of the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

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

Question 11

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 19.6t + 2. At $$what time $$t$$ does the ball reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

Question 12

Which of the following is the correct simplified form of the expression $$\log_{2} 8 + \log_{2} 4$$?

Accepted Answer

$$5$$

Question 13

Given the rational function $$f(x) = \frac{x^2$ - 4}{x^2$ - 1}$$, which of the following describes its vertical asymptotes?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 14

A student is asked to solve the equation $$2(x-3) = 4x + 6. $$What is the value of $$x$$?

Accepted Answer

$$x = -6$$

Question 15

Which of the following is the correct solution to the system of equations: $$\begin{cases} x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(4, 3)$$

Question 16

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

Accepted Answer

$$9$$

Question 17

Which of the following is the correct solution to the equation $$\sqrt{x+5} = 4$$?

Accepted Answer

$$x = 11$$

Question 18

A real-world application: The population of a bacteria culture is modeled by $$P(t) = 500e$$^{0.3t}$$, where t$ is in hours. What is the population after 5 hours (rounded to the nearest whole number)?

Accepted Answer

Approximately $$2241$$

Question 19

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

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