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

Study Guide - Practice Questions