Question 1

Which of the following equations represents a circle with center at $$(-3, 2)$$ and radius $$5$$?

Accepted Answer

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

Question 2

Given the function $$f(x) = 2x + 3$$, what is $$f^{-1}(x$$)$$, the inverse function?

Accepted Answer

$$ f$$^{-1}$$(x) = \frac{x - 3}{2} $$

Question 3

A company charges a set-up fee of $$225, then 6.75$ per shirt to produce new t-shirts. Which function C(x$$)$$ models the total cost of producing x$ shirts?

Accepted Answer

$$ C(x) = 225 + 6.75x $$

Question 4

Which of the following best describes the transformation from $$y = \sqrt{x} to$$ $$y = -2\sqrt{x - 3} + 1$$?

Accepted Answer

Shift right 3 units, reflect over the $$x-$$axis, vertically stretch by 2, shift up 1 unit

Question 5

Solve for $$x$$: $$3x^2 - 4x - 5 = 0$

Accepted Answer

$$ x = \frac{4 \pm \sqrt{16 + 60}}{6} $$

Question 6

Which of the following is the domain of the function $$f(x) = \frac{1}{x^2$ - 4x + 3}$$?

Accepted Answer

$$ (-\infty, 1) \cup (1, 3) \cup (3, \infty) $$

Question 7

A population of 7,500 people is experiencing exponential growth at a rate of 2.5% per year. Which equation models the population $$P$$ after $$t$$ years?

Accepted Answer

$$ P = 7500(1.025)^t $$

Question 8

Which of the following best describes the symmetry of the graph of $$y = x^2$?

Accepted Answer

Symmetric with respect to the $$y-$$axis

Question 9

Solve the system of equations: $$\begin{cases} 2x + y = 5 \ x - y = 1 \end{cases}$$

Accepted Answer

$$ x = 2,\ y = 1 $$

Question 10

Given $$f(x) = x^2$ - 4x + 3$$, which of the following is a $$y-$$intercept of the graph?

Accepted Answer

$$ (0, 3) $$

Question 11

Which of the following is the solution to the inequality $$2x - 3 \u003e 7$$?

Accepted Answer

$$ x \u003e 5 $$

Question 12

If $$f(x) = x^2$ - 6x + 8$$, what are the $$x-$$intercepts of the graph?

Accepted Answer

$$ x = 2,\ x = 4 $$

Question 13

Which of the following is the equation of a line parallel to $$y = 3x + 5$$ and passing through the point $$(4, -2)$$?

Accepted Answer

$$ y = 3x - 14 $$

Question 14

Given $$f(x) = x^2$ - 4x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$ (2, -1) $$

Question 15

Solve for $$x$$: $$\frac{2x - 1}{3} = 5$$

Accepted Answer

$$ x = 8 $$

Question 16

Which of the following is the solution to the equation $$|2x - 5| = 9$$?

Accepted Answer

$$ x = 7,\ x = -2 $$

Question 17

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

Accepted Answer

$$ [0, \infty) $$

Question 18

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

Accepted Answer

$$ 9 $$

Question 19

Which of the following is the solution set for the inequality $$x^2 - 9$$ \u003c 0$$?

Accepted Answer

$$ (-3, 3) $$

Question 20

Which of the following is the factored form of $$x^2 - 5x + 6$?

Accepted Answer

$$ (x - 2)(x - 3) $$

College Algebra Final Exam Review: Comprehensive Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard