Question 1

Which of the following is the correct solution to the equation $$2(x-4) + 3(x+4) = 2x - 5$$?

Accepted Answer

$$x = 5$$

Question 2

What are the $$x-$$intercepts of the function $$g(x) = x^2$ - 4$$?

Accepted Answer

$$(2, 0)$$ 	ext{ and } (-2, 0)$

Question 3

Solve the quadratic equation $$3x^2 - 7 = 2x$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = \frac{2 \pm \sqrt{25}}{6}$$

Question 4

An architect is allowed 15 square yards of floor space for a rectangular bedroom. The width must be 7 yards less than twice the length. What are the length and width?

Accepted Answer

Question 5

Which of the following is the correct solution to $$\sqrt{2x+1} + 7 = x$$?

Accepted Answer

$$x = 8$$

Question 6

Solve the compound inequality $$-3 \u003c \frac{x-7}{4} \leq 5$$ and express the solution in interval notation.

Accepted Answer

$$(-15, 27]$$

Question 7

Find the difference quotient $$\frac{f(x+h)-f(x)}{h}$$ for $$f(x) = 3x^2$ + 7.$$

Accepted Answer

$$6x + 3h$$

Question 8

What is the equation of the line passing through $$(4, -1)$$ and $$(6, 2) in $$slope-intercept form?

Accepted Answer

$$y = \frac{3}{2}x - 7$$

Question 9

Given $$f(x) = 3x^2$ + 5x$$ and $$g(x) = x + 7$$, what is $$(f - g)(x)$$?

Accepted Answer

$$3x^2 + 5x - x - 7$

Question 10

Let $$f(x) = \frac{2}{x-5}. $$What is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x) = 5$$ + \frac{2}{x}$$

Question 11

What is the standard form of the circle centered at $$(7, -3)$$ with radius $$4$$?

Accepted Answer

$$(x-7)^2$$ + $$(y+3)^2 = 16$

Question 12

Given $$f(x) = \frac{7}{x-1}$$ and $$g(x) = x-3$$, what is $$(f \circ g)(x)$$ and its domain?

Accepted Answer

$$(f \circ g)(x) = \frac{7}{x-4}$$, domain: $$(-\infty, 4) \cup (4, \infty)$$

Question 13

The equation $$x^2$$ + $$y^2 + 4x - 2y - 4 = 0$ represents a circle. What is its center and radius after completing the square?

Accepted Answer

Center: $$(-2, 1)$$, radius: $$3$$

Question 14

Which transformation(s) describe how $$g(x) = (\frac{1}{2}x)^3$ is obtained from f(x$$) = $$x^3$$?

Accepted Answer

Horizontal stretch by factor $$2$$

Question 15

What is the domain of $$g(x) = 3\sqrt{-x-2}$$?

Accepted Answer

$$(-\infty, -2]$$

Question 16

Find the distance between the points $$(-\frac{2}{3}, \frac{5}{2})$$ and $$(\frac{5}{6}, \frac{1}{2}).$$

Accepted Answer

$$\frac{\sqrt{65}}{6}$$

Question 17

Which of the following is the correct solution to $$|2x-1| \u003c 5 in $$interval notation?

Accepted Answer

$$(-2, 3)$$

Question 18

What is the equation of the line perpendicular to $$7x - 5y + 3 = 0$$ and passing through $$(-2, 3) in $$slope-intercept form?

Accepted Answer

$$y = \frac{5}{7}x + \frac{31}{7}$$

College Algebra Review #1 – Step-by-Step Study Guidance

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