Free Printable Test 11 Review: Rational Equations & Functions (22-23)

1.

Solve for x.

a)

-4

b)

0

c)

$\frac{1}{2}$

d)

4

2.

Try on your own. Solve for y.

a)

-1

b)

0

c)

1

d)

-2

3.

Solve!

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

4.

a)

1/7

b)

47/36

c)

7

d)

23

5.

Solve for x

a)

6

b)

17/5

c)

19/2

d)

- 6

6.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

7.

Solve for x

a)

1/3

b)

-5.5

c)

5.5

d)

2.5

8.

Solve the equation for x.

a)

7

b)

6

c)

14

d)

0

9.

Solve.

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

10.

Solve.

a)

x = 4.5

b)

x = -4.5

c)

x = 3

d)

x = -3

11.

Solve the equation for x.

a)

6

b)

12

c)

0

d)

3

12.

a)

x = 8.9

b)

x = 16

c)

x = 9

d)

x = 12

13.

a)

3/5

b)

3/4

c)

1/4

d)

4/5

14.

a)

2

b)

1

c)

-1

d)

-4

15.

Solve $\frac{x-2}{3x}=\frac{1}{3x}+2$

a)

0

b)

$-\frac{3}{5}$

c)

-2

d)

$-\frac{1}{5}$

16.

$\frac{2n+16}{n-8}=\frac{1}{2n-16}-\frac{1}{2}$

a)

$-\frac{23}{5}$

b)

$7$

c)

$-4$

d)

$\frac{4}{3}$

17.

$\frac{7x-49}{x^2+8x+12}=\frac{3}{x+6}+\frac{1}{x+2}$

a)

$-2$

b)

$5$

c)

$6$

d)

$\frac{61}{3}$

18.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

19.

Identify the LCD.

a)

x²(x - 2)

b)

x(x - 2)

c)

x

d)

(x - 2)

20.

Solve for x

a)

x = 10

b)

x = $-\frac{30}{13}$

c)

x = 6

d)

no solution

21.

Solve and check for extraneous solutions

a)

x= - 3 &x= -8

b)

x= -3

c)

No Solution

d)

x= -8

22.

Solve

a)

k = 1, k = 5

b)

k = −1, k = 5

c)

k = −1, k = −3

d)

k = 1

23.

How do you know when a solution is extraneous?

a)

When you plug in the solution, there is 0 in a numerator.

b)

When you plug in the solution, there is 0 in a denominator.

c)

When the solution is x = 0

d)

It looks extra. 💁‍♀️

24.

Which of the following below would be an extraneous solution to the equation?

a)

$x\ =\ 9$

b)

$x\ =\ -3$

c)

$x\ =\ -9$

d)

$x\ =\ 1$

25.

Which of the following below would be an extraneous solution to the equation?

a)

$x\ =\ 3$

b)

$x\ =\ 5$

c)

$x\ =\ 1$

d)

$x\ =\ -5$

26.

Which of the following below would be an extraneous solution to the equation?

a)

$x\ =\ 2$

b)

$x\ =\ 7$

c)

$x\ =\ 14$

d)

$x\ =\ -2$

27.

Which of the following below would be an extraneous solution to the equation?

a)

$x\ =\ 2$

b)

$x\ =\ -4$

c)

$x\ =\ 6$

d)

$x\ =\ -66$

28.

Which of the following below would be an extraneous solution to the equation?

a)

$x\ =\ 1$

b)

$x\ =\ -1$

c)

$x\ =\ -2$

d)

$x\ =\ -6$

29.

Which of the following below would be an extraneous solution to the equation?

a)

$x\ =\ 1$

b)

$x\ =\ -1$

c)

$x\ =\ 0$

d)

$x\ =\ -6$

30.

Which of the following below would be an extraneous solution to the equation?

a)

$x\ =\ -3$

b)

$x\ =\ -2$

c)

$x\ =\ 10$

d)

$x\ =\ 5$

31.

A boat goes 10 miles downstream in the same time it can go 3 miles upstream. The speed of the current is 2 miles per hour. Which equation could you use to find the speed of the boat in still water?

a)

$\frac{10}{2-x}=\frac{3}{2+x}$

b)

$\frac{10}{x-2}=\frac{3}{x+2}$

c)

$\frac{10}{x+2}=\frac{3}{x-2}$

d)

$\frac{10}{2+x}=\frac{3}{2-x}$

32.

A plane flies 1225 miles with a tailwind in the same time it can go 1100 miles against the wind. The speed of the plane in still air is 575 miles per hour. Which equation would you use to find the speed of the wind?

a)

$\frac{1225}{575-x}=\frac{1100}{575+x}$

b)

$\frac{1225}{575+x}=\frac{1100}{575-x}$

c)

$\frac{1225}{x+575}=\frac{1100}{x-575}$

d)

$\frac{1225}{x-575}=\frac{1100}{x+575}$

33.

A car travels 400 km in the same time that a freight train travels 300 km. The speed of the car is 25 km/h more than the speed of the train. Find the speed of the car and the speed of the train. (Hint set fractions equal rather than adding to a set time.)

a)

$\frac{400}{x-25}=\frac{300}{x+25}$

b)

$\frac{400}{x+25}=\frac{300}{x-25}$

c)

$\frac{400}{x+25}=\frac{300}{x}$

d)

$\frac{400}{x}=\frac{300}{x+25}$

34.

The time it takes for a canoe to go 4 miles upstream and back 4 miles downstream is 5 hours. The current in the lake is 2 mile per hour. Find the average speed (rate) of the canoe in still water.

a)

$\frac{4}{x+2}+\frac{4}{x-2}=5$

b)

$\frac{4}{2+x}+\frac{4}{2-x}=5$

c)

$\frac{4}{x+2}=\frac{5}{x-2}$

d)

$\frac{4}{2+x}=\frac{5}{2-x}$

35.

What are the asymptotes for the following rational function?

$f\left(x\right)\ =\ \frac{6x}{2x+1}$ ?

a)

$y\ =3,\ x\ =\ \frac{1}{2}$

b)

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

c)

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

d)

$y=\frac{1}{2},\ x\ =\ 3$ y=1/2

36.

Rewrite the following rational expression to identify the asymptotes.

f\left(x\right)\ =\ \frac{2x}{x+4}

a)

$y=2,\ x\ =-4$

b)

$y=-4,\ \ x\ =2$

c)

$y=2,\ x=4$

d)

$y=4,\ x=2$

37.

Find the Vertical Asymptotes for the following function

g\left(x\right)\ =\frac{2x^2+x-9}{x^2-2x-8}

a)

$x=-4,\ x=2$

b)

$x=-2,\ x=4$

c)

$x=-6,\ x\ =\ -2$

d)

$x=\ 2,\ x=6$

38.

What is the horizontal asymptote of the following function?

f\left(x\right)=\frac{3x^2}{4x^2-1}

a)

$y=\frac{3}{4}$

b)

$y=\frac{4}{3}$

c)

$y=0$

d)

No asymptote

39.

What is the horizontal asymptote for the following function?

f\left(x\right)=\frac{4x+3}{x^2-4}

a)

$y=4$

b)

$y=\frac{1}{4}$

c)

$y=0$

d)

No Asymptote

40.

What is the horizontal asymptote for the following function?

f\left(x\right)=\frac{5x^3+6}{x^2-9x+19}

a)

$y=5$

b)

$y=\frac{1}{5}$

c)

$y=0$

d)

No Asymptotes

41.

What is the x-intercept of the graph?

a)

x= 1

b)

x= -3

c)

y= -3

d)

x= 0

42.

What are the asymptotes for the graph pictured?

a)

x= 1

y= 1

b)

x= 0

y= 0

c)

none

d)

x= -1

y= 1

43.

What is the horizontal asymptote for the following function?

f\left(x\right)=\frac{5x^3+6}{x^2-9x+19}

a)

$y=5$

b)

$y=\frac{1}{5}$

c)

$y=0$

d)

No Asymptotes

44.

Find the Vertical Asymptotes for the following function

g\left(x\right)\ =\frac{2x^2+x-9}{x^2-2x-8}

a)

$x=-4,\ x=2$

b)

$x=-2,\ x=4$

c)

$x=-6,\ x\ =\ -2$

d)

$x=\ 2,\ x=6$

45.

Given the following rational function, determine the y-intercept. $\frac{x+3}{-3x-6}$

a)

y = -3

b)

y = 3

c)

y = -1/2

d)

no y-intercept

46.

Given the following rational function, determine the x-intercept. $\frac{x+3}{-3x-6}$

a)

x = -3

b)

x = 3

c)

x = -1/2

d)

no x-intercept

47.

What are the coordinates of the hole, if one exists.

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

48.

What are the x and y intercepts?

a)

(4, 0) and (0, -4)

b)

(-4, 0) and (0, -4)

c)

(-4, 0) and (0, 4)

d)

(0, 0) and (0, -4)

49.

Solve: $\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$

a)

$x=-5$

b)

$x=5$

c)

$\frac{5}{\left(x+5\right)\left(x-5\right)}$

d)

No Solution

50.

What are the asymptotes

a)

x=1, x= 2, y =1, y= 2

b)

x= 1, x=-1, y = 1

c)

x=1 y =1

d)

x=-1, y =1, y =-1

51.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

52.

What are the coordinates of the hole, if one exists.

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

53.

g(x), h(x), and f(x) all mean

a)

x=

b)

y=

54.

The range are the _____ values.

a)

y

b)

x

c)

Both x and y

55.

The domain are the ______ values.

a)

y

b)

x

c)

Both x and y

56.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

end behavior

d)

none

57.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

58.

Does the rational function have any discontinuities? $y=\frac{x^2-3x-4}{x-2}$ Select all that apply.

a)

$x=2$ is a hole

b)

$x=2$ is a vertical asymptote

c)

$x=4$ is a vertical asymptote

d)

$x=-1$ is a vertical asymptote

59.

Does the rational function have any discontinuities? $y=\frac{2x+2}{x^2-1}$ Select all that apply.

a)

$x=1$ is a hole

b)

$x=1$ is a vertical asymptote

c)

$x=-1$ is a hole

d)

$x=-1$ is a vetical asymptote

60.

What is the y-intercept of the rational equation? $y=\frac{x-4}{2-x}$

a)

(0,-2)

b)

(0,4)

c)

(0,2)

d)

(0,-4)

61.

What are the x-intercepts of the rational expression below. $y=\frac{2x^2+7x+3}{x^2+4x+2}$ Select all that apply.

a)

$(0,0)$

b)

$(-3,0)$

c)

$\left(\frac{1}{2},0\right)$

d)

$\left(-\frac{1}{2},0\right)$

62.

Which of the following does not have a horizontal asymptote?

a)

$y=\frac{2x^3+7x^2+3x}{x^2+4x+4}$

b)

$y=\frac{x-3}{x^2+x-12}$

c)

$y=\frac{x-4}{2-x}$

d)

they all have a horizontal asymptote

63.

What is the horizontal asymptote of the rational equation below? $y=\frac{3x^2+15x+18}{x^2+4x-5}$

a)

$y=\frac{1}{3}$

b)

$y=3$

c)

$y=0$

d)

$y=1$

Test 11 Review: Rational Equations & Functions (22-23)

Total questions: 63

Worksheet time: 2hrs 34mins

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