Question 1

Which of the following points is a solution to the equation $$3x - 2y = 6$$?

Accepted Answer

$$(2, 0)$$

Question 2

Find the $$x- $$and $$y-$$intercepts of the line $$3x + 2y = 12.$$

Accepted Answer

$$x-$$intercept: $$(4, 0)$$, $$y-$$intercept: $$(0, 6)$$

Question 3

Given the endpoints of a diameter of a circle at $$(2, -3)$$ and $$(6, 5)$$, what is the length of the radius?

Accepted Answer

$$\sqrt{17}$$

Question 4

Find the equation of the circle with center at $$(3, -2)$$ and radius $$5.$$

Accepted Answer

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

Question 5

Which of the following correspondences is NOT a function?

Accepted Answer

A relation where one $$x-$$value maps to two different $$y-$$values

Question 6

Find the domain of the function $$f(x) = \sqrt{7 - x}.$$

Accepted Answer

$$(-\infty, 7]$$

Question 7

Given the cost function $$C = 20x + 20000$$, how many items must be produced if costs reached $$144,000$$?

Accepted Answer

$$6,200$$

Question 8

Find the slope and $$y-$$intercept of the equation $$2y - 4x = 8.$$

Accepted Answer

Slope: $$-2$$, $$y-$$intercept: $$4$$

Question 9

Determine if the lines $$y = 2x + 3$$ and $$2y - 4x = 8$$ are parallel, perpendicular, or neither.

Accepted Answer

Parallel

Question 10

For the piecewise function $$f(x) = \begin{cases} x + 2, & x \u003c 1 \ 3x - 1, & x \geq 1 \end{cases}$$, find $$f(0).$$

Accepted Answer

$$2$$

Question 11

How is the graph of $$f(x) = \sqrt{x}$$ transformed to obtain $$g(x) = \sqrt{x - 3} + 2$$?

Accepted Answer

Shifted right 3 units and up 2 units

Question 12

Find the domain and range of the function $$f(x) = x^2$ - 4.$$

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[-4, \infty)$$

Question 13

Given $$f(x) = x^2$ and g(x) = x + 1$, find (f - g)(2$$)$$.

Accepted Answer

$$1$$

Question 14

Which of the following best describes the transformation from $$y = x^2$ to y = -2(x$$ - $$1)^2 + 3$?

Accepted Answer

Reflected over the $$x-$$axis, vertically stretched by 2, shifted right 1 unit and up 3 units

Question 15

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, find (f$$ \circ g)(2)$$.

Accepted Answer

$$9$$

Question 16

Which of the following intervals describes where the function $$f(x) = -x^2$ + 4 is $$increasing?

Accepted Answer

$$(-\infty, 0)$$

Question 17

Given the equation $$x^2$$ + $$y^2 = 49$, what is the center and radius of the circle?

Accepted Answer

Center: $$(0, 0)$$, Radius: $$7$$

Question 18

Which of the following equations represents a line perpendicular to $$y = -\frac{1}{2}x + 3$$?

Accepted Answer

$$y = 2x - 1$$

Question 19

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

Accepted Answer

$$2x + h$$

College Algebra Exam 1 Review: Study Notes and Key Concepts

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