Free Printable Reasoning with Functions 1 Unit 2 Review

1.

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, -3, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 3

2.

a)

y = -x⁴ + 5x³ + 2

b)

y = -x³

c)

y = x³ - 3x - 2

d)

y = -x³ + 3x + 2

3.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

4.

Factor: x²+9x-10

a)

(x-5)(x+2)

b)

(x+5)(x-2)

c)

(x+10)(x-1)

d)

(x-10)(x+1)

5.

What is the degree of the function:

f(x) = 6x² + 4 - 3x⁴ + 5x - 9x³

a)

1

b)

2

c)

3

d)

4

6.

If f(x) = 4x³ + 5x² - 3, find f(-2).

a)

-415

b)

-15

c)

-55

d)

-615

7.

What is the vertex of the equation

y=\left(x-3\right)^2+5

a)

(-3, 5)

b)

(3, 5)

c)

(-3, -5)

d)

(3, -5)

8.

What is the vertex of the equation

y=\left(x+7\right)^2+3

a)

(7, 3)

b)

(7, -3)

c)

(-7, 3)

d)

(-7, -3)

9.

Given the equation for this parabola:
y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

10.

Find the y-intercept of this graph?

a)

(-4,0)

b)

(0,-4)

c)

(4,0)

d)

(0,4)

11.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

12.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

13.

Which of the following is the Factored(Root) Form of a quadratic function?

a)

f(x) = mx + b

b)

f(x) = ax² + bx + c

c)

f(x) = a(x - m)(x - n)

d)

f(x) = a(x - h)² + k

14.

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

a)

(-5, 0) and (9, 0)

b)

(5,0) and (-9, 0)

c)

(5, 0) and (9, 0)

d)

(-3, 0) and (5, 0)and (-9, 0)

15.

Which equation is the standard form of a quadratic function?

a)

f(x) = mx + b

b)

f(x) = a(x - m)(x - n)

c)

f(x) = ax² + bx + c

d)

f(x) = a(x - h)² + k

16.

Tyler wants to know HOW HIGH the soccer ball will get if he kicks it straight up in the air.

When looking at the graph on GeoGebra, which value should he find?

a)

x-value at the vertex

b)

y-value at the vertex

c)

where the curve hits the x-axis (positive x-intercept)

17.

What can you find easily using the standard form of a quadratic equation?

a)

The vertex

b)

The x-intercepts

c)

The y-intercept

d)

The axis of symmetry

18.

Ceiran wants to know when his model rocket will HIT THE GROUND.

When looking at the graph on GeoGebra, which should he find?

a)

x-value at the vertex

b)

y-value at the vertex

c)

where the curve hits the x-axis (positive x-intercept)

19.

Neha is trying to find HOW MANY SECONDS it will take a golf ball TO GET TO ITS HIGHEST POINT after being hit on the golf course.

Which should she look for?

a)

x-value at the vertex

b)

y-value at the vertex

c)

where the curve hits the x-axis (positive x-intercept)

20.

Which is the best estimate for when the football hits the ground?

a)

0.5 seconds

b)

4.0 seconds

c)

1.5 seconds

d)

2.7 seconds

21.

Which best describes the HEIGHT of the football at 2 seconds?

a)

10 feet

b)

22 feet

c)

6 feet

d)

31 feet

22.

What is the vertex and what does it mean?

a)

At 1.4 seconds the football is at a maximum height of 31 ft

b)

At 31 seconds the football is at a maximum height of 1.4 ft

c)

The ball is at its maximum height at 2.7 seconds

d)

The hits the ground at 1.4 seconds.

23.

What does the Y-INTERCEPT and what does it mean?

a)

The ball is thrown from an initial height of 1.4 feet.

b)

The ball reaches a maximum height of 6 feet.

c)

The ball hits the ground at 6 seconds.

d)

The ball is thrown form an initial height of 6 feet.

24.

Find the Vertex:
y = x² + 6x + 2

a)

(-3,-7)

b)

(1,6)

c)

(6,2)

d)

No Real Solution

25.

The graph of a quadratic function is called a

a)

Parabola

b)

Vertex

c)

Axis of Symmetry

d)

Vertex Form

26.

What causes the graph of y = x² to open downward?

a)

multiply the x² by a fraction

b)

multiply the x² by a decimal

c)

multiply the x² by a negative number

d)

multiply the x² by a number greater than 1

27.

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

28.

If the blue graph is

f(x) = x²

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 parabola has a vertex at (1,6) and passes through (3,-18). Write the equation in vertex form.

Formula: f(x) = a(x - h)²+ k

a)

f(x) = 3(x - 1)²- 18

b)

f(x) = -6(x - 1)²+ 6

c)

f(x) = 6(x - 3)²- 18

d)

f(x) = -3(x + 1)²- 6

30.

What is the formula to find the vertex of a parabola?

a)

x = $\frac{-b}{2}$

b)

x = -b

c)

x = $\frac{-b}{\left(2a\right)}$

d)

x = -2b

31.

What steps transform the graph y = x² to y = x² + 8

a)

shifted up 8 units

b)

shifted down 8 units

c)

shifted left 8 units

d)

shifted right 8 units

32.

What steps transform the graph y = x² to y = (x-4)²

a)

Shifted down 4 units

b)

Shifted left 4 units

c)

Shifted right 4 units

d)

Shifted up 4 units

33.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

34.

Describe the transformation of y = f(x) for the new function
y = f(x) - 5

a)

The graph of y = f(x) was shifted to the right 5 units.

b)

The graph of y = f(x) was shifted to the left 5 units.

c)

The graph of y = f(x) was shifted up 5 units.

d)

The graph of y = f(x) was shifted down 5 units.

35.

Describe the transformation of y = f(x) for the new function y = f(x) + 5

a)

The graph of y = f(x) was shifted to the right 5 units.

b)

The graph of y = f(x) was shifted to the left 5 units.

c)

The graph of y = f(x) was shifted up 5 units.

d)

The graph of y = f(x) was shifted down 5 units.

36.

f^-1(x) is written when...

a)

The inverse is not a function

b)

The function fails the HLT

c)

The inverse is a function

d)

There are two different functions

37.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

38.

Find the domain and range of the function
Hint: Use a scratch graph to help you visualize things.

a)

Domain: (-∞, ∞) Range: [-∞, 4]

b)

Domain: [1, ∞) Range: (-∞, 4]

c)

Domain: [-1. ∞) Range: [4, ∞)

d)

Domain: [4, ∞) Range: [-1,∞)

39.

Find the cube root.

a)

9

b)

3

c)

-9

d)

-3

40.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

(-∞, 0)

d)

[ 0, ∞)

41.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function becomes the domain of its inverse.

d)

The domain of a function becomes the range of its inverse.

42.

Re-write the expression in radical form.
x^2/3

a)

∛x²

b)

√x³

c)

(1/x)

d)

∛x

43.

Suppose a function $f\left(x\right)$ has domain $\left[3,\infty\right)$ and range $\left[0,\infty\right)$ . What is the domain of $f^{-1}\left(x\right)$ ?

a)

$\left(-\infty,3\right]$

b)

$\left(-\infty,\ 0\right]$

c)

$\left[0,\ \infty\right)$

d)

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

44.

a)

2^3/5

b)

-2^3/5

c)

2^5/3

d)

8⁵

45.

a)

(5x)^-2/1

b)

(5x)^2/1

c)

(5x)^-1/2

d)

(5x)^1/2

46.

Rewrite the following expression

a)

4^1/2

b)

4

c)

1

d)

4^2/4

47.

100^1/2 = ?

a)

50

b)

10

c)

100.5

d)

20

48.

Re-write the expression in radical form.
x^2/3

a)

(∛x)²

b)

√x³

c)

(1/x)

d)

∛x

49.

Simplify

a)

b)

c)

d)

50.

$\frac{x^3y}{xy^5}$

a)

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

b)

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

c)

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

d)

$\frac{2x^2}{y^5}$

51.

a)

m⁴

b)

m⁶

c)

m¹⁰

d)

1/m⁶

52.

Rewrite using a positive exponent.
g^-7

a)

¹/_g⁷

b)

g⁷

c)

¹/_g^-7

d)

-g⁷

53.

Rewrite as a positive exponent: 4^-2

a)

16

b)

-16

c)

$\frac{1}{16}$

d)

$-\frac{1}{16}$

54.

Which of the following can be used to find Average Rate of Change?

a)

$\frac{y_2-y_1}{x_2-x_1}$

b)

$\frac{x_2-x_1}{y_2-y_1}$

c)

$y=mx+b$

d)

$\frac{\Delta y}{\Delta x}$

e)

$y_2-y_1=m\left(x_2-x_1\right)$

55.

f(x) = 2x² + 12x + 16

What is the average rate of change of f(x) on the interval [3, 5].

(a)

56.

Average rate of change is also known as...

a)

the y-intercept

b)

slope

c)

a function

d)

domain

57.

Which function needs to have a restricted domain so that its inverse is a function?

a)

quadratic

b)

square root

58.

Find the inverse function of $y=x^2+9$ for a domain of $\left[0,\infty\right)$

*Hint. Check in a new tab with desmos

a)

$y=\left(x+9\right)^2$

b)

$y=\sqrt{x-9}$

c)

$y=\sqrt{x}-9$

d)

$y=\sqrt{x+9}$

59.

Find the inverse function of $f\left(x\right)=\sqrt{x}-6$

*Hint. Check in a new tab with desmos

a)

$y=\left(x+6\right)^2$ , $x\ge-6$

b)

$y=\left(x-6\right)^2$ , $x\ge6$

c)

$y=x^2+6$ , $x\ge0$

d)

$y=x^2+36$ , $x\ge0$

60.

Are the graphs inverses?

a)

yes

b)

no

61.

Which polynomial is written in standard form?

a)

-3x + 8x² + 9x³ - 11

b)

9x³ + 8x²- 3x - 11

c)

8x²+ 9x³ -11 - 3x

d)

-11 - 3x + 8x² + 9x³

62.

Solve the equation by factoring.

a)

x = {3,8}

b)

x = {-3,8}

c)

x = {3,-8}

d)

x = {-3,-8}

63.

What is the quadratic formula?

a)

b)

c)

d)

64.

If each mark on the x-axis represents one second, when did the object reach its maximum height?

a)

2.5 seconds

b)

2 seconds

c)

5.5 seconds

d)

3 seconds

65.

If each mark on the x-axis represents one second, when did the object reach the ground?

a)

2.5 seconds

b)

6 seconds

c)

5.5 seconds

d)

5 seconds

66.

The object was thrown or launched from what position?

a)

At the ground

b)

Above the ground

c)

Below the ground

67.

Solve the following quadratics equation by quadratic formula.

x² + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

68.

$27^{\frac{1}{3}\ \ }$ is the same as

a)

$27\ \times\ \frac{1}{3}\$ so the value is 9

b)

$\ ^3\sqrt{27}\$ so the value is 3

69.

$8^{\frac{1}{3}}\ \$ is the same as

a)

$\ ^3\sqrt{8}\ \$ so the value is 2

b)

$8\ \times\ \frac{1}{3}\$ so the value is $\ \ \frac{8}{3}\ \$

70.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

71.

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

a)

10x²

b)

18x² + 4

c)

6x² + 4

72.

If you rewrite this expression to a radical, where would the 5 go?

32 ^3/5

a)

inside the $\sqrt{ }$

b)

outside the $\sqrt{ }$

c)

it disappears

73.

a)

y⁴

b)

y⁵

c)

y⁶

d)

6^y

74.

Simplify

a)

7a⁵/b³

b)

b³/7a⁵

c)

7b³/a^-⁵

d)

7b³ /a⁵

75.

a)

t²⁴

b)

t¹²

c)

t¹⁸

d)

t^-12

76.

Simplify using the 9 Laws of Exponents:

a)

b)

c)

d)

77.

Simplify using exponent rules.

a)

x^1/2

b)

x^4/2= x²

c)

x^5/4

d)

x^6/2= x³

78.

Simplify each expression so that it contains only positive exponents.

a)

b)

c)

d)

79.

Given the function f(x)= 4x²- 5, find a formula for the average rate of change on the interval, [t, t+2].

Hint: You would need to substitute into the function t+2 and reduce to an expression. Then substitute t. Both expressions will become your y₂and y₁values respectively. Last, use the rate of change, definition $\frac{y_2-y_1}{x_2-x_1}$ .

a)

8t + 8

b)

8t

c)

4(t+2)² - 5

80.

Given the function f(x)= 4x²- 5, find f(t+2). Don't Simplify.

a)

8t + 8

b)

8t

c)

4(t+2)² - 5

81.

Simplify 4(t+2)² - 5. Hint: Use Orders of Operations to Simplify.

a)

4t²+ 64t -5

b)

4t²+ 16t + 11

c)

4t²+ 64t + 59

82.

Solve the equation. Make sure to check for extraneous solutions. $\sqrt{x+4}=x-2$

a)

x = 0

5 is extraneous

b)

x = 5

0 is extraneous

c)

x = -2

3 is extraneous

d)

x = 3

-2 is extraneous

83.

Solve the equation. Make sure to check for extraneous solutions.

$\sqrt{4x}=x-3$

a)

x = 1

9 is extraneous

b)

x = 3

-2 is extraneous

c)

x = 9

1 is extraneous

d)

x = -2

3 is extraneous

84.

What is true about an extraneous solution?

a)

Not a true solution to the original problem that are extra.

b)

It can emerge during the solving process as an additional answer, making the equation false.

c)

It needs to be checked after solving the original problem.

d)

All of the above

85.

Given the y-intercept of the graph being (0,-24) What would be the scale value for the polynomial function? Hint: For visual purposes, the x-intercepts are at -6, 5, and 8. Place these values in factored form and solve for the missing a-value.

a)

a = -1

b)

a = 1

c)

a= -2

86.

Solve using the quadratic formula...

9x² = 4 + 7x

a)

b)

c)

d)

No solution

87.

What is the "c" value in the equation..

4x^2=18

a)

4

b)

18

c)

0

d)

-18

88.

$x^2-5x\ -14\ =\ 0$

Determine the x-intercepts by completing the quadratic formula.
$x=\ \frac{5\ \pm\sqrt{\left(-5\right)^2-4\left(1\right)\left(-14\right)}}{2\left(1\right)}$

a)

$x=\frac{5\pm\sqrt{-31}}{2}$

b)

$x\ =\ -7,\ x\ =\ 2$

c)

$x\ =\ 7,\ x\ =\ -2$

d)

$no\ solution$

89.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

90.

The height, h (in feet), of a ball t seconds after it is thrown upward is given by the equation h=-16t²+60t+5. What does the constant term 5 in the equation represent?

a)

time required for the ball to hit the ground

b)

time required for the ball to reach the highest point

c)

height after 5 seconds

d)

height when first thrown

Reasoning with Functions 1 Unit 2 Review

Total questions: 90

Worksheet time: 5hrs 2mins

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