Question 1

Given the points $$(2,1)$$ and $$(-4.5,3.2)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(2 + 4.5)^2$ + (1 - 3.2)^2$} = \sqrt{6.5^2$ + (-2.2)^2$} = \sqrt{42.25 + 4.84} = \sqrt{47.09}$$

Question 2

What is the equation of the line passing through $$(2,1)$$ with slope $$-2/3 in $$point-slope form?

Accepted Answer

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

Question 3

Find the $$x-$$intercept of the line $$4x - 5y = -20.$$

Accepted Answer

$$(-5, 0)$$

Question 4

Given the equation $$x^2$$ + $$(y-1)^2 = 4$, what are the center and radius of the circle?

Accepted Answer

Center $$(0,1)$$, radius $$2$$

Question 5

Which of the following equations represents a circle with center $$(1,-2)$$ and radius $$3$$?

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Which of the following is the equation of a line parallel to $$2x - 3y = 4$$ passing through $$(5, -6)$$?

Accepted Answer

$$y + 6 = \frac{2}{3}(x - 5)$$

Question 8

Given $$f(x) = \frac{x^2$}{2x+1}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, -\frac{1}{2}) \cup (-\frac{1}{2}, \infty)$$

Question 9

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

Accepted Answer

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

Question 10

Is the function $$f(x) = \frac{x^2$}{2x+1}$$ even, odd, or neither?

Accepted Answer

Neither even nor odd

Question 11

What is the effect of the transformation $$f(x) 	o f(x) + 2 on $$the graph of $$f(x)$$?

Accepted Answer

Shifts the graph up by 2 units

Question 12

If $$f(x) = x^2$ - 4x + 1$$, what is the absolute minimum value and where does it occur?

Accepted Answer

Minimum at $$x = 2$$, value $$-3$$

Question 13

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

Accepted Answer

$$(x+2)^2 - 4(x+2) + 1$$ = $$x^2 + 4x + 4 - 4x - 8 + 1$$ = $$x^2 - 3$

Question 14

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

Accepted Answer

$$3x^2 - 12x + 3$

Question 15

What is the $$y-$$intercept of the function $$f(x) = \frac{x^2$}{2x+1}$$?

Accepted Answer

$$(0,0)$$

Question 16

Which transformation will shift the graph of $$f(x)$$ left by 2 units?

Accepted Answer

$$f(x+2)$$

Question 17

Given $$y = 2\sqrt{x}$$, which transformation is applied to the base function $$y = \sqrt{x}$$?

Accepted Answer

Vertical stretch by a factor of 2

Question 18

For the function $$f(x) = x^3$, which transformation will reflect the graph over the x$-axis and shift it up by 3 units?

Accepted Answer

$$-f(x) + 3$$

College Algebra Study Notes: Linear Equations, Circles, Functions, and Transformations

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