Free Printable Function Operations and Properties

1.

What is the domain of

$\sqrt[]{x^2-49}$

a)

$\left[-7,7\right]$

b)

$\left(-\infty,-7\right)\cup\left(7,\infty\right)$

c)

$\left(-7,\ 7\right)$

d)

$\left(-\infty,\ -7\right]\cup\left[7,\infty\right)$

2.

What is the domain?

a)

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

b)

$\left(-\infty,4\right)\left(4,\infty\right)$

c)

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

d)

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

3.

What is the domain of $f\left(x\right)=\left(x+7\right)^2-13$ ?

a)

All real numbers

b)

$-10.606\le x\le-3.394$

c)

All real numbers greater than -13

d)

$-10.606\le y\le-3.394$

4.

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

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

5.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

6.

$f\left(x\right)=3x-2;\ Find\ f\left(x-1\right)$

a)

$3x-8$

b)

$3x^2-2$

c)

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

d)

$3x-5$

7.

Which equation would you use to find

f\left(0\right)

a)

Top

b)

Middle

c)

Bottom

8.

Please find

f\left(2\right)

a)

0

b)

4

c)

-1

d)

-8

9.

Evaluate

f\left(-5\right)

a)

-6

b)

-4

c)

-11

d)

23

10.

What is the value of $\lfloor-3.4\rfloor$

a)

-2

b)

-3

c)

-4

d)

0

11.

What is the value of $\lfloor2.9\rfloor$

a)

0

b)

2

c)

3

d)

2.9

12.

Describe the transformation from the parent graph

a)

Reflect over x, right 3, down 4

b)

Reflect over y, right 3, down 4

c)

Reflect over x, right 3, up 4

d)

Reflect over y, left 3, down 4

13.

Describe the parent graph transformation

a)

stretch by 1/2, left 1, down 3

b)

stretch by 1/2, right 1, down 3

c)

compression by 1/2, left 1, down 3

d)

compression by 1/2, right 1, down 3

14.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

15.

Identify the parent function.

a)

$y=\sqrt{x}$

b)

$y=x$

c)

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

d)

16.

What is the parent function seen here?

a)

Logarithmic

b)

Exponential

c)

Square Root

d)

Constant Function

17.

Identify the parent function of the graph.

a)

Rational

b)

Logarithmic

c)

Exponential

d)

Square Root

18.

Which piecewise function matches this graph?

a)

b)

c)

d)

19.

Graph

a)

b)

c)

d)

20.

What value of b would make the function continuous? $\left\{2x^2-9,\ x<3\right\}\left\{bx+3,\ x\ge3\right\}$

a)

1

b)

2

c)

3

d)

4

21.

Which classification is given to a function that exhibits symmetry over the y-axis?

a)

odd

b)

even

22.

Use the symmetry tests to determine the type of symmetry for: $x=y^2-4$
i. symmetric with respect to the x-axis
ii. symmetric with respect to the y-axis
iii. symmetric with respect to the line y=x

iv. symmetric with respect to the origin

a)

i only

b)

ii, and iv

c)

iii only

d)

i, ii, iii, and iv

23.

Find the inverse of $f\left(x\right)=3x+2$

a)

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

b)

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

c)

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

d)

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

24.

Is the inverse of this a function?

a)

No

b)

Yes

25.

What is the inverse of the given quadratic function? $f\left(x\right)=4\left(x+3\right)^2$ when $x\ge-3$

a)

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

b)

$f^{-1}\left(x\right)=\sqrt{4x+3}$

c)

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

d)

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

Function Operations and Properties

Total questions: 25

Worksheet time: 6hrs 15mins

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