Free Printable Functions and Relations

1.

Which relation is not a function?

a)

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

b)

{(2,7), (3,7), (4,7), (5,8)}

c)

{(1,-5), (-1,6), (1,5), (6,-3)}

d)

{(3,-2), (5,-6), (7,7), (8,8)}

2.

Which relation is a function?

a)

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

b)

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

c)

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

d)

{(1,2), (2,2), (3,2), (1,3)}

3.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

4.

a)

Function

b)

Not a Function

5.

Is this table a function or not a function?

a)

Function

b)

Not a Function

6.

Which of the following equations is not a function?

a)

$x=10$

b)

$y=5$

c)

$y=6x+1$

d)

$y=x^2$

7.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

8.

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

c)

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

9.

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}

10.

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

11.

given f(x) = $\frac{3x+2}{x-1}$ , What is f(1)?

a)

-5

b)

5

c)

0

d)

f(1) is undefined

12.

What is f(5) for the function f?

f(x) = 2(x - 7)

a)

3

b)

-4

c)

-3

d)

1

13.

If f(x) = 5 + 4(x – 4)²,

what is f(7)?

a)

81

b)

29

c)

41

d)

54

14.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f+g\right)\left(x\right)=$

a)

$5x^2+1$

b)

$5x^2-3$

c)

$6x+1$

d)

$6x-3$

15.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f\cdot g\right)\left(x\right)=$

a)

$5x-3$

b)

$5x^2+2$

c)

$5x^2-7x+2$

d)

$5x-7$

16.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(\frac{f}{g}\right)\left(x\right)$

a)

$\frac{x-1}{5x-2}$

b)

$\frac{5x-2}{x-1}$

c)

$\frac{-1}{3}$

d)

$-3$

17.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(f\cdot g\right)\left(x\right)=$

a)

$3x^4-24x^3+8x^2+32x-16$

b)

$3x^4-8x-16$

c)

$3x^4-24x^3+8x^2-32x-16$

d)

$3x^4-24x^3+16x^2+32x-16$

18.

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

19.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(\frac{f}{g}\right)\left(x\right)$

a)

$\frac{x-1}{5x-2}$

b)

$\frac{5x-2}{x-1}$

c)

$\frac{-1}{3}$

d)

$-3$

20.

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

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

21.

Find $\left(\frac{f}{g}\right)\left(x\right)$

a)

$x^2-x+3$

b)

$x^2+x-13$

c)

$-x^3+8x^2+5x-40$

d)

$\frac{x^2-5}{-x+8},\ x\ne8$

22.

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

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

23.

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)

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

24.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

25.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

26.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

27.

Simplify

a)

(n-2)/(n+2)

b)

(n+2)/(n-2)

c)

1/(n+2)

d)

1/(n-2)

28.

Multiply and Simplify

a)

5a-25/ (a-5)(a+9)

b)

5/(a+9)

c)

5a-25/ (a+9)

d)

1/(a+9)

29.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

30.

$Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}$

a)

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

b)

$\frac{x}{x-3}$

c)

$\frac{x+6}{x-3}$

d)

$\frac{x}{x+6}$

Functions and Relations_TVL Jeremiah

Total questions: 30

Worksheet time: 3hrs 30mins

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