Free Printable College Algebra Chapter 3 Review

1.

Which set of points represents a function?

a)

{(1, 3) , (5, 1) , (7,1)}

b)

{(1, 1), (5, 1), (8,1), (1, 7)}

2.

What is standard form of a quadratic?

a)

$ax^2+bx+c$

b)

$mx+b$

c)

$a\left(x-h\right)^2+k$

d)

$ax+by=c$

3.

What is vertex form of a quadratic?

a)

$ax^2+bx+c$

b)

$mx+b$

c)

$a\left(x-h\right)^2+k$

d)

$ax+by=c$

4.

What is the vertex of $f\left(x\right)=4x^2-8x+1$ ?

a)

(1, -3)

b)

(-3, 1)

c)

x=1

d)

I don't know

5.

Find the vertex of the quadratic function: y = 4x²+ 24x + 5

a)

(−3, −31)

b)

(3, 113)

c)

(−3, −76)

d)

(3, 5)

6.

Find the Vertex:
f(x) = x² + 10x + 21

a)

(-5,-4)

b)

(1,10)

c)

(10,21)

d)

No Real Solution

7.

Find the Vertex:
y = x² + 6x + 2

a)

(-3,-7)

b)

(1,6)

c)

(6,2)

d)

No Real Solution

8.

Match the equation to its description.

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

9.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a reflection across the line x = -4

b)

a reflection across the line y = -4

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

10.

Which equation describes the transformation of shifting

f\left(x\right)=x^2

two units right?

a)

$x^2+2$

b)

$\left(x+2\right)^2$

c)

$x^2-2$

d)

$\left(x-2\right)^2$

11.

Does $f\left(x\right)=x^2-3x-10$ open up or down?

a)

Up

b)

Down

12.

What direction does $f\left(x\right)=-4x^2-10x+1\$ open?

a)

Up

b)

Down

13.

What direction does $f\left(x\right)=5x^2-10x+10$ open?

a)

up

b)

down

14.

What direction does $f\left(x\right)=-4x^2$ open?

a)

Up

b)

Down

15.

What value do we look at to determine the direction a parabola opens?

a)

a

b)

b

c)

c

16.

Based on the graph, is the a value of the function positive or negative?

a)

positive

b)

negative

17.

Based on the graph, is the a value of the function positive or negative?

a)

positive

b)

negative

18.

What is the y-intercept of $f\left(x\right)=5x^2-9x+18$

a)

5

b)

-9

c)

18

19.

What is the y-intercept of $f\left(x\right)=7x^2-10x+4$

a)

7

b)

4

c)

-10

20.

What value of $ax^2+bx+c$ determines the y-intercept?

a)

a

b)

b

c)

c

21.

What is the vertex of $f\left(x\right)=-x^2+5x-3$ ?

a)

$\left(\frac{5}{2},\ \frac{13}{4}\right)$

b)

$\left(-\frac{5}{2},\ -\frac{87}{4}\right)$

c)

$\left(0,\ 3\right)$

d)

$\left(\frac{5}{2},\ 0\right)$

22.

Is the vertex of $f\left(x\right)=-x^2+5x-3$ a maximum or minimum?

a)

Maximum

b)

Minimum

c)

d)

23.

How do we find the vertex of a parabola?

a)

$\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

b)

$\left(-\frac{b}{2a},\ f\left(-\frac{b}{2a}\right)\right)$

c)

Factoring

d)

you can't

24.

Evaluate the function when x = 4

a)

f(4) = 2(4) - 5 = 3

b)

f(4) = 2(4) - 5 = -1

c)

f(4) = ½(4) + 1 = 3

d)

f(4) = 4

25.

What is g(-2) if:

a)

-7

b)

7

c)

1

d)

-1

26.

What is g(-2) if:

a)

-7

b)

7

c)

1

d)

-1

27.

Find f(0)

a)

-3

b)

18

c)

4

d)

0

28.

Evaluate this function for x=2

a)

f(2) = 4

b)

f(2) = 3

c)

f(2) = -3

d)

f(2) = 5

29.

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

30.

Identify the transformation from the graph of f(x)=x²to the graph g(x)= -(x+5)²

a)

shifted up five units
reflection in x-axis

b)

shifted down five units
reflection in x-axis

c)

shifted left 5 units
reflection x-axis

d)

shifted right 5 units
reflection x-axis

31.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

32.

Find the domain of each function.

f\left(x\right)=\frac{3x}{x+3}

a)

$\left(-\infty,\ 3\right)∪\left(3,\infty\right)$

b)

$\left(-\infty,0\right)∪\left(0,\infty\right)$

c)

$\left(-\infty,\ -3\right)∪\left(-3,\infty\right)$

d)

$\left(-\infty,\ -3\right)∪\left(0,\infty\right)$

33.

Find the domain of each function.

f\left(x\right)=\frac{8x-16}{x-64}

a)

$\left(-\infty,64\right)∪\left(64,\ \infty\right)$

b)

$\left(-\infty,-8\right)∪\left(8,\ \infty\right)$

c)

$\left(-\infty,\ -64\right)∪\left(64,\ \infty\right)$

d)

$\left(-\infty,-8\right)∪\left(-8,8\right)\ \cup\left(8,\ \infty\right)$

34.

Find the domain of

f\left(x\right)\ =\ \frac{x-3}{x+4}

.

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,3\right)\cup\left(3,\infty\right)$

c)

$\left(-\infty,-4\right)\cup\left(-4,\infty\right)$

d)

$\left(-\infty,-4\right)\cup\left(-4,3\right)\cup\left(3,\infty\right)$

35.

Find the domain of the function.

f\left(x\right)=\frac{x+3}{x-1}

a)

$\left(-\infty,\ -3\right)∪\left(-3,\ \infty\right)$

b)

$\left(-\infty,1\right]\ ∪\ \ \left[1,\infty\right]$

c)

$\left(-\infty,1\right)∪\left(1,\infty\right)$

d)

$\left(-\infty,\ -1\right)∪\left(-1,\infty\right)$

36.

Find the domain of the function.

f\left(x\right)=\frac{x+3}{5x}

a)

$\left(-\infty,\ -3\right)∪\left(-3,\ \infty\right)$

b)

$\left(-\infty,5\right)\ ∪\ \ \left(5,\infty\right)$

c)

$\left(-\infty,0\right)∪\left(0,\infty\right)$

d)

$\left(-\infty,\ -1\right)∪\left(-1,\infty\right)$

37.

Find the domain of each function.

f\left(x\right)=\frac{x}{x^2-121}

a)

$\left(-\infty,11\right)∪\left(11,\ 11\right)\cup\left(11,\infty\right)$

b)

$\left(-\infty,-11\right)∪\left(-11,\ 11\right)\cup\left(11,\infty\right)$

c)

$\left(-\infty,-11\right)\cup\left(11,\infty\right)$

d)

$\left(-\infty,121\right)∪\left(121,\infty\right)$

38.

Find the domain of

f\left(x\right)\ =\ x-3

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,3\right)\cup\left(3,\infty\right)$

c)

$\left(-\infty,-4\right)\cup\left(-4,\infty\right)$

d)

$\left(-\infty,-4\right)\cup\left(-4,3\right)\cup\left(3,\infty\right)$

39.

Find the domain of each function.

f\left(x\right)=\frac{x^2+5x-6}{x^2+10x+24}

a)

$\left(-\infty,-6\right)∪\left(-6,\ 1\right)\cup\left(1,\infty\right)$

b)

$\left(-\infty,-6\right)∪\left(-6,\ -4\right)\cup\left(-4,\infty\right)$

c)

$\left(-\infty,4\right)∪\left(4,\ 6\right)\cup\left(6,\infty\right)$

d)

$\left(-\infty,-6\right)∪\left(-4,\infty\right)$

40.

Find the domain of each function.

f\left(x\right)=\frac{3x+12}{x^2-6x}

a)

$\left(-\infty,-4\right)∪\left(-4,\ 6\right)\cup\left(6,\infty\right)$

b)

$\left(-\infty,-4\right)∪\left(-4,\ -2\right)\cup\left(-2,\infty\right)$

c)

$\left(-\infty,0\right)∪\left(0,\ 6\right)\cup\left(6,\infty\right)$

d)

$\left(-\infty,6\right)∪\left(6,\infty\right)$

41.

Find the domain of each function.

f\left(x\right)=\sqrt{3x-21}

a)

$\left[7,\infty\right]$

b)

$\left[3,\infty\right)$

c)

$\left[7,\infty\right)$

d)

$\left[21,\infty\right)$

42.

Find the domain of each function.

f\left(x\right)=\sqrt{8x+40}

a)

$\left[-5,\infty\right]$

b)

$\left(-5,\infty\right)$

c)

$\left[-5,\infty\right)$

d)

$\left[5,\infty\right)$

43.

Find the domain of

f\left(x\right)\ =\ \frac{x-3}{\sqrt{x+4}}

.

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,3\right)\cup\left(3,\infty\right)$

c)

$\left(-4,\infty\right)$

d)

$\left[-4,\infty\right)$

44.

Find the domain of each function.

f\left(x\right)=x^2-6x+8

a)

$\left(-\infty,2\right)∪\left(-4,\ 2\right)\cup\left(-4,\infty\right)$

b)

$\left(-\infty,-4\right)∪\left(-4,\ -2\right)\cup\left(-2,\infty\right)$

c)

$\left(-\infty,2\right)∪\left(2,\ 4\right)\cup\left(4,\infty\right)$

d)

$\left(-\infty,\ \infty\right)$

College Algebra Chapter 3 Review

Total questions: 44

Worksheet time: 1hrs 28mins

Similar Resources on Wayground