Free Printable IM2H Midterm Review

1.

On which interval(s) is the given function increasing?

a)

(-∞, 2) U (-2, ∞)

b)

(-2, 2) U (-2, ∞)

c)

(-∞, -2) U (0.5, ∞)

d)

(0, 2) U (0.5, ∞)

2.

State the domain and range using "inequality" notation.

a)

x ≥ -4 and y ≥ 2

b)

x ≥ 4 and y ≥ 2

c)

x > -4 and y > 2

d)

D: [-4, ∞) and R: [2, ∞)

3.

Describe the intervals over which the given function is decreasing.

a)

(-∞, 0) U (2, ∞)

b)

(5, -4) U (2, -3)

c)

(-3, 0) U (2, 3)

d)

(5, -4) U (0, -3)

4.

How would you describe the behavior of this function on the domain interval (-1, 1)?

a)

increasing

b)

decreasing

c)

constant

5.

Describe the interval over which the given function is decreasing.

a)

(-∞, 4)

b)

(4, 3)

c)

(0, 1)

d)

(0, -∞)

6.

What is the local max?

a)

(0, 36)

b)

(-2.55, -6.55), (2.55, -6.55)

c)

(-∞, ∞)

d)

None

7.

How would you describe the point at (0,6)?

a)

Relative Minimum

b)

Absolute Minimum

c)

Relative Maximum

d)

Absolute Maximum

8.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

9.

Evaluate f(0)

a)

0

b)

19

c)

9

d)

-19

10.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

11.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

12.

Find f(0)

(a)

13.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

14.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

15.

What is the domain interval for the green piece of this function?

a)

-2 < x ≤ 1

b)

-1 < x ≤ 0.5

c)

x > -2

d)

x ≤ 1

16.

Which graph matches:

-x+4 if x<2

2x-6 if x>=2

a)

A

b)

B

c)

C

d)

D

17.

Using the pictured graph, what is the equation of the blue line?

a)

$\frac{1}{2}x\ +3$

b)

$x$

c)

-1

d)

-x

18.

Which piecewise function matches this graph?

a)

b)

c)

d)

19.

Using the pictured graph, what is f(2)?

a)

-3

b)

-1

c)

1

d)

3

20.

Was the inverse function found correctly?

a)

no

b)

yes

21.

When using composition to check whether two functions are inverses, $g\left(f\left(x\right)\right)$ and $f\left(g\left(x\right)\right)$ must both equal...

a)

$x$

b)

$y$

c)

$f\left(x\right)$

d)

$g\left(x\right)$

22.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

23.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

24.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

25.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $f\left(g\left(x\right)\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

26.

If $f\left(x\right)=2x+3$ and $g\left(x\right)=-3x-4$ , find $f\left(g\left(x\right)\right)$

a)

$-6x^2-17x-12$

b)

$6x^2+x-12$

c)

$-6x-5$

d)

$5x+7$

27.

When $f(x)=9-3x$ and $g(x)=5x-7$ , find $\left(f(g(x)\right)$

a)

$14x-10$

b)

$-8x+2$

c)

$30-15x$

d)

$2x-2$

28.

.
If the blue is f(x)=x^2,then the red must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

29.

a)

g(x)=2x²

b)

g(x)=0.5x²

c)

g(x)=x²+2

d)

g(x)=(x+2)²

30.

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

31.

$y=3\left|x\right|$

Which graph represents this transformed function

a)

b)

c)

d)

32.

$y=\sqrt{x}-2$

Which graph represents this transformed function

a)

b)

c)

d)

33.

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

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

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

d)

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

34.

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

a)

a vertical translation 4 units up

b)

a vertical translation 4 units down

c)

a horizontal translation 4 units to the left

d)

a horizontal translation 4 units to the right

35.

In the equation $f\left(x\right)=5\left(x+3\right)^2-10$ what does the $5$ do?

a)

Vertical stretch by 5

b)

Horizontal compress by 5

c)

Reflect

d)

Move up 5

36.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

37.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

38.

Compare the function y = 5x² to the parent function y = x²

a)

Wider

b)

Narrower

39.

$f\left(x\right)=\left(\frac{1}{2}x\right)^2-3$ What transformations does the function have from the parent function $f\left(x\right)=x^2$

a)

Horizontal compression by 1/2 Vertical Translation Down 3

b)

Horizontal stretch by 2 Vertical Translation Up 3

c)

Horizontal stretch by 2 Vertical Translation Down 3

d)

Horizontal compression by 1/2 Vertical Translation Down 3

40.

$g\left(x\right)=\left(3x-9\right)^2+2$ Check ALL that apply: What transformations have occured to the function?

a)

Translation up 2

b)

Translation right 3

c)

Horizontally Compressed by 1/3

d)

Horizontally stretched by 3

e)

Translated right 9

41.

Find the local maximum and minimum

a)

Local max at x = -3

Local min at x = -3

b)

Local max at x = 1

Local min at x = -3

c)

Local max at x = -3

Local min at x = 1

d)

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

42.

Identify the local minimum

a)

x = 8

b)

x = 4

c)

$\infty$

d)

x = 2

43.

Identify the location of the global (or absolute) maximum.

a)

$x=-2$

b)

$x=1$

c)

$x=\infty$

d)

$x=-\infty$

44.

What is the location of the absolute maximum for the graphed function?

a)

x = 1

b)

x = 3

c)

x = 4

d)

x = 5

e)

Does Not Exist

45.

What is the value of the absolute minimum for the following function?

$f\left(x\right)=\left(x-2\right)^2-4$

a)

-4

b)

0

c)

2

d)

4

e)

Does Not Exist

46.

What is the location of the relative maximum within the given interval of the graphed function?

-5\le x\le0

a)

x = -4

b)

x = -2

c)

x = 0

d)

x = 3

e)

Does Not Exist

47.

What are the extrema of the graph?

a)

Max = (2, -3), (1, 2)

Min = (-3, -1), (-1, 4)

b)

Max = (-3, -1), (-1, 4)

Min = (2, -3), (1, 2)

c)

Max = (-1, -3), (4, -1)

Min = (-3, 2), (2, 1)

d)

Max = (-3, 2), (2, 1)

Min = (-1, -3), (4, -1)

48.

How many extrema are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

d)

3 increasing intervals, 2 decreasing intervals

e)

2 increasing intervals, 3 decreasing intervals

49.

How many extrema (max and mins) are in the picture?

a)

2

b)

3

c)

4

d)

5

50.

What is the relative max?

a)

x = 0

b)

x = -2.55

c)

(-∞, ∞)

d)

None

51.

What is the increasing interval for the function below?

a)

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

b)

$\left(-\infty,2\right]$

c)

$\left(-\infty,6\right]$

d)

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

52.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

53.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

54.

Which of the following relations is a one-to-one function?

a)

{(1,2), (1,4), (1,5), (1,6)}

b)

{(4,-5), (3,-5), (2,8), (1,8)}

c)

{(-3,-2), (3,4), (-1,-2), (-1,5)}

d)

{(10,9), (8,7), (6,5), (4,3)}

55.

Determine which function is one-to-one?

a)

b)

c)

d)

56.

Determine which function is NOT one-to-one

a)

b)

c)

d)

57.

$x+y\ge3$

a)

b)

c)

d)

58.

$x+y\ge3$

a)

b)

c)

d)

59.

$x+3>y$

a)

b)

c)

d)

60.

a)

$x\ge1$

b)

$x>1$

c)

$y\ge1$

d)

$y>1$

61.

a)

$x+3y\le6$

b)

$x-3y\le6$

c)

$3x-y\le6$

d)

$3x+y\le6$

62.

Identify the CORRECT linear inequalities that satisfies the feasible region.

a)

$y<x$

b)

$y\ge4$

c)

$x\ge4$

d)

$y\ge0$

63.

Identify the CORRECT linear inequalities that satisfy the feasible region.

a)

$y\ge x-1$

b)

$y>3$

c)

$y<6$

d)

$y\ge0$

64.

Identify the CORRECT linear inequalities that satisfy the feasible region.

a)

$y\ge0$

b)

$y\ge2$

c)

$x<2$

d)

$4x+y>4$

65.

Which statement is FALSE?

a)

A dashed line includes all the point on the line

b)

A solid line includes all the point on the line

c)

A feasible region that is not enclosed is call open half-plane.

d)

A feasible region that is enclosed is call closed half-plane.

66.

Simplify: $3n^5\cdot5n^{10}$

a)

$15n^5$

b)

$8n^{15}$

c)

$15n^{50}$

d)

$15n^{15}$

67.

Simplify: $\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$

a)

$16a^8b^9c^9$

b)

$8a^8b^9c^9$

c)

$8a^6b^5c^6$

d)

$16a^5b^5c^6$

68.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

69.

Simplify: $\left(3x^5\right)^6$

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

70.

Simplify: $\left(3x^5\right)^6$

a)

$18x^{30}$

b)

$729x^{11}$

c)

$3^6x^{30}$

d)

$729x^{30}$

71.

Simplify: $\left(4y\right)^{-3}$

a)

$\frac{1}{64y^3}$

b)

$64y^{-3}$

c)

$-12y^{-3}$

d)

$\frac{64}{y^3}$

72.

Simplify: $2m^{-1}$

a)

$\frac{1}{2m}$

b)

$\frac{m}{2}$

c)

$\frac{2}{m}$

d)

$2m$

73.

Simplify: $\frac{50r^6n^{-7}}{2n^2r^4}$

a)

$25r^4n^5$

b)

$\frac{25r^4}{n^5}$

c)

$\frac{25r^2}{n^9}$

d)

$25r^2n^{-9}$

74.

Simplify the expression:

a)

25x²y³

b)

-5xy² ∛5x

c)

5ixy² ∛5x

d)

-125x³y⁶ ∛5x

75.

Simplify the expression:

a)

3y⁴∜5x³y³

b)

9xy∜5xy³

c)

121.5x^.75y^1.75

d)

3y∜5x³y³

76.

Simplify the expression:

a)

6x²y² ∛3

b)

6xy² ∛6x²

c)

∛1296x⁵y⁶

d)

cannot combine; unlike radicand

77.

Simplify the expression:

a)

√2 - 3√3

b)

2√-59

c)

-2√2 - 3√3

d)

-3.782

78.

Simplify the expression:

a)

11√5 + 2∛5

b)

√365 + ∛40

c)

13√5

d)

9√5

79.

Simplify the expression:

a)

-15 + 8√9

b)

9

c)

2 + 8√3 + 6√6

d)

9 + 14√3

80.

Simplify the radical expression:
$\sqrt{128a^3b^4}$

a)

$8ab^2\sqrt{2a}$

b)

$2a\sqrt{8ab^2}$

c)

$2ab\sqrt{64ab}$

d)

$64ab^2\sqrt{2a}$

IM2H Midterm Review

Total questions: 80

Worksheet time: 3hrs 45mins

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