$$x \in \mathbb{R}, x \neq 2, x \neq -2$$

$$f(3) = 3^2$ - 4 \times 3 + 1 = 9 - 12 + 1 = -2$$

$$f(0) = 0^2$ - 4 \times 0 + 1 = 1$$

Question 1

Given the points $$A(2, 3)$$ and $$B(5, 7)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(5-2)^2$ + (7-3)^2$} = \sqrt{9 + 16} = \sqrt{25} = 5$$

Question 2

Find the slope of the line passing through the points $$(-1, 4)$$ and $$(3, -2).$$

Accepted Answer

$$m = \frac{-2 - 4}{3 - (-1)} = \frac{-6}{4} = -\frac{3}{2}$$

Question 3

What is the equation of the circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

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

Question 4

Which of the following is the equation of a line parallel to $$y = 2x + 1$$ and passing through $$(4, -3)$$?

Accepted Answer

$$y = 2x - 11$$

Question 5

Given the function $$f(x) = \frac{1}{x^2$ - 4}$$, what is its domain?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 2, x 
eq -2$$

Question 6

For the function $$f(x) = x^2$ - 4x + 1$$, what is the value of $$f(3)$$?

Accepted Answer

$$f(3) = 3^2$ - 4 	imes 3 + 1 = 9 - 12 + 1 = -2$$

Question 7

Given $$f(x) = x^2$ - 4x + 1$$, find all $$x$$ such that $$f(x) = 13.$$

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 8

Which of the following describes the transformation from $$y = f(x) to$$ $$y = f(x) + 2$$?

Accepted Answer

Vertical shift up by 2 units

Question 9

Given $$f(x) = \frac{1}{x}$$, which of the following statements is true about its symmetry?

Accepted Answer

$$f(x) is an $$odd function

Question 10

Find the $$y-$$intercept of the function $$f(x) = x^2$ - 4x + 1.$$

Accepted Answer

$$f(0) = 0^2$ - 4 	imes 0 + 1 = 1$$

Question 11

Given the function $$f(x) = \sqrt{x}$$, which transformation results in $$y = -2\sqrt{x}$$?

Accepted Answer

Vertical stretch by a factor of 2 and reflection over the $$x-$$axis

Question 12

For the function $$f(x) = x^2$ - 4x + 1$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 2 + \sqrt{3}$$ and $$x = 2 - \sqrt{3}$$

Question 13

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

Accepted Answer

$$x \in \mathbb{R}, x 
eq 3$$

Question 14

If $$f(x) = x^2$, what is the effect of the transformation g(x) = f(x-2) + 3$?

Accepted Answer

Shift right by 2 units and up by 3 units

Question 15

Given $$f(x) = x^2$ - 4x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -3)$$

Question 16

Which of the following is the equation of a circle with center $$(-1, 4)$$ and radius $$3$$?

Accepted Answer

$$(x + 1)^2$ + (y - 4)^2$ = 9$$

Question 17

For the function $$f(x) = \frac{1}{x^2$ + 1}$$, what is its range?

Accepted Answer

$$0 \u003c f(x) \leq 1$$

Question 18

Which of the following lines is perpendicular to $$y = \frac{1}{2}x + 3$$ and passes through $$(0, 1)$$?

Accepted Answer

$$y = -2x + 1$$

Question 19

Given $$f(x) = x^2$ - 4x + 1$$, for which values of $$x is $$the function decreasing?

Accepted Answer

$$x \u003c 2$$

College Algebra Study Guide: Functions, Graphs, and Equations

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