Free Printable F4 Functions

1.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

2.

Is the relation a function?
{(4,5), (4,-7), (4,2), (4,0), (4,9)}

a)

Yes

b)

No

3.

Is the relation a function?
{(4,5), (4,-7), (4,2), (4,0), (4,9)}

a)

Yes

b)

No

4.

Is this table a function or not a function?

a)

Function

b)

Not a Function

5.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

6.

Evaluate f(-2) if f(x) = x²+ 3.

a)

-1

b)

1

c)

7

d)

-7

7.

Is relation shown a function?

a)

YES

b)

NO

8.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

9.

Which image is NOT the graph of a function?

a)

b)

c)

d)

10.

What is the domain in inequality notation?

a)

( -4 , 4 )

b)

[ 1 , -3 )

c)

-4 < x < 4

d)

1 ≥ y > -3

11.

What is the range in inequality notation?

a)

[ -2 , 2 )

b)

( 5 , 1 ]

c)

-2 ≤ x < 2

d)

5 > y ≥ 1

12.

What is the range of the table?

a)

{-4, 0, 1, 3}

b)

{-2, 0, 2, 3}

c)

{-4, -2, 0, 1, 2, 3}

d)

{ (0, 0), (2, -4), (3, 3), (-2, 1) }

13.

What is the domain of the graph?

a)

-6 ≤ x ≤ 6

b)

0 ≤ x ≤ 7

c)

2 ≤ x ≤ 7

d)

No Solution

14.

What is the definition of function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

15.

All of the y values or outputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

16.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

17.

Which of these is NOT the same

a)

Range

b)

Input

c)

Dependent Value

d)

Y-Value

18.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

19.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

20.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D:{0, 1, 2, -4}
R:{1, -3, -4}

c)

D:{0, 1, 2, 3, 4}
R:{1, -3, -4}

21.

a)

8

b)

-24

c)

24

d)

-22

22.

a)

27

b)

21

c)

24

d)

72

23.

a)

Function

b)

Not a Function

24.

a)

Function

b)

Not a Function

25.

If f(x) = 3x^2 - 2x + 1 and g(x) = x - 4, what is (f*g)(x)?

a)

3x^3 - 14x^2 + 9x - 4

b)

3x^3 - 10x^2 + 5x - 4

c)

3x^3 - 12x^2 + 8x - 5

d)

3x^3 - 16x^2 + 7x - 3

26.

What is the formula for function multiplication?

a)

(f*g)(x) = f(x) + g(x)

b)

(f*g)(x) = f(x) - g(x)

c)

(f*g)(x) = f(x) * g(x)

d)

(f*g)(x) = f(x) / g(x)

27.

If f(x) = x^2 + x and g(x) = 3x + 1, what is the value of f(g(4))?

a)

150

b)

172

c)

182

d)

200

28.

What is the standard form of a quadratic function?

a)

f(x) = ax^2 + bx + c, where a, b, and c are constants.

b)

f(x) = a(x - h)^2 + k, where (h, k) is the vertex.

c)

f(x) = a(x + b)(x - c), where b and c are roots.

d)

f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

29.

If g(x) = 3x + 4 and h(x) = 3x - 1, what is g(h(x))?

a)

9x + 1

b)

9x + 7

c)

6x + 4

d)

12x + 3

30.

What is the definition of function composition?

a)

Function composition is the operation of applying one function to the results of another, defined as (f∘g)(x) = f(g(x)).

b)

Function composition is the process of adding two functions together to create a new function.

c)

Function composition involves multiplying two functions to find their product.

d)

Function composition is the method of finding the inverse of a function.

31.

What is the definition of function subtraction?

a)

Function subtraction is the operation of adding one function to another, defined as (f+g)(x) = f(x) + g(x).

b)

Function subtraction is the operation of multiplying one function by another, defined as (f*g)(x) = f(x) * g(x).

c)

Function subtraction is the operation of subtracting one function from another, defined as (f-g)(x) = f(x) - g(x).

d)

Function subtraction is the operation of dividing one function by another, defined as (f/g)(x) = f(x) / g(x).

32.

What does f(g(x)) represent?

a)

The sum of f(x) and g(x).

b)

The product of f(x) and g(x).

c)

The composition of functions, where g(x) is substituted into f(x).

d)

The difference between f(x) and g(x).

33.

a)

-1

b)

1

c)

-1/3

d)

-5/3

34.

a)

5

b)

25

c)

√23

d)

31

35.

a)

A.

b)

B.

c)

C.

d)

D.

36.

a)

A.

b)

B.

c)

C.

d)

D.

37.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

38.

Let f(x) = 2x - 1, g(x) = 3x, and h(x) = x² + 1. Compute: (h ^og)(x)

a)

3x² + 3

b)

-1

c)

6x - 3

d)

9x² + 1

39.

If a function has the point (4,-2) then its inverse must have which point?

a)

(-4,-2)

b)

(-4,2)

c)

(-2,4)

d)

(2,-4)

40.

a)

9 - √17

b)

4

c)

2

d)

√8

41.

If f^-1(-25) = 7 then what is f(7) =

a)

25

b)

7

c)

No enough information.

d)

-25

42.

Which is f^-1(x)?

a)

f^-1(x)=4(x+3)³

b)

f^-1(x)=(4x+12)³

c)

f^-1(x)=3+1/4(x)³

d)

f^-1(x)=1/4(x+3)³

43.

FInd the inverse of the function.
$f\left(x\right)=\frac{3x-15}{2}$

a)

$f^{-1}\left(x\right)=-x-5$

b)

$f^{-1}\left(x\right)=3x+5$

c)

$f^{-1}\left(x\right)=\frac{15+2x}{3}$

d)

$f^{-1}\left(x\right)=\frac{2}{3}x-\frac{19}{3}$

44.

If f(x)=3x, what is f^-1(x)?

a)

x/3

b)

3x²

c)

3x + 3x

d)

3x^-1

45.

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

46.

What does an inverse function do?

a)

Nothing

b)

Makes it bigger

c)

Does the opposite of the original function

47.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

48.

If f(x)=x+5, what is f^-1(x)?

a)

(x + 5)²

b)

x - 5

c)

(x + 5)^-1

d)

undefined

49.

Find the inverse of $f(x)=2x+1$

a)

$f^{-1}(x)=2x$

b)

$f^{-1}(x)=\frac{x-1}{2}$

c)

$f^{-1}(x)=2$

50.

Find the inverse of $f(x)=\frac{x-5}{3}$

a)

$f^{-1}(x)=\frac{3}{5}+x$

b)

$f^{-1}(x)=3x+5$

c)

$f^{-1}(x)=5x+3$

51.

Find the inverse of $f(x)=\frac{1}{x}$ .

a)

$f^{-1}\left(x\right)=\frac{1}{x}$

b)

$f^{-1}\left(x\right)=x$

c)

no solution

52.

f(x) is a function with the following steps:

1. Multiply by 2

2. Square the quantity

3. Add 9

What is the equation for f(x)?

a)

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

b)

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

c)

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

53.

Select the two expressions which are inverses of each other:

a)

$x-4$

b)

$4x$

c)

$\frac{x}{4}$

d)

$\frac{4}{x}$

54.

Select the two expressions which are inverses of each other:

a)

$\sqrt{x+2}$

b)

$\sqrt{x-2}$

c)

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

d)

$\sqrt{x}-2$

55.

Select the option that shows the steps for this function in order: $f\left(x\right)=\frac{\sqrt{x+6}}{3}$

a)

1. Add 6 to x
2. Square the quantity
3. Divide by 3

b)

1. Take the square root of x
2. Add 6
3. Divide by 3

c)

1. Add 6 to x
2. Take the square root of the quantity
3. Divide by 3

d)

1. Square x
2. Add 6
3. Divide by 3

56.

If $f\left(x\right)=\frac{\sqrt{x+6}}{3}$ , select the correct steps for the INVERSE function in the correct order

a)

1. Multiply by 3

2. Take the square root of the quantity
3. Add 6

b)

1. Square x
2. Subtract 6
3. Multiply by 3

c)

1. Subtract 6
2. Square the quantity
3. Multiply by 3

d)

1. Multiply by 3
2. Square the quantity
3. Subtract 6

57.

Select the option that shows the steps for this function in order: $f\left(x\right)=7\left(x+4\right)^2$

a)

1. Add 4 to x
2. Square the quantity
3. Multiply by 7

b)

1. Square x
2. Add 4
3. Multiply by 7

c)

1. Add 4 to x
2. Multiply by 7
3. Square the quantity

58.

If $f\left(x\right)=7\left(x+4\right)^2$ , select the correct steps for the INVERSE function in the correct order

a)

1. Subtract 4

2. Take the square root of the quantity
3. Divide by 7

b)

1. Divide by 7
2. Take the square root of the quantity
3. Subtract 4

c)

1. Take the square root of x
2. Subtract 4
3. Divide by 7

59.

If f(x) is a function with the following steps:

1. Add 3

2. Multiply by 5

What is the function?

a)

f(x) = 5x + 3

b)

f(x) = 3x + 5

c)

f(x) = 5(x + 3)

d)

f(x) = 3(x+5)

60.

If f(x) is a function with the following steps:

1. Add 3

2. Multiply by 5

How would we write the inverse function, f ^-1(x)?

a)

$f^{-1}\left(x\right)=\frac{x-3}{5}$

b)

$f^{-1}\left(x\right)=3-\frac{x}{5}$

c)

$f^{-1}\left(x\right)=\frac{x}{5}-3$

d)

$f^{-1}\left(x\right)=5\left(x+3\right)$

F4 Functions

Total questions: 60

Worksheet time: 4hrs 14mins

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