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Radical functions and rational exponents

Total questions: 25

Worksheet time: 3hrs 54mins

Name
Class
Date
1.
 Solve the equation.
a)
36
b)
18
c)
-18
d)
27
2.
a)
16
b)
4
c)
508/3
d)
116/9
3.
Solve:
(x+2)2/3 + 3 = 7
a)
x=7
b)
x=5
c)
x=6
d)
x=9
4.
Simplify: 
a)
∛121
b)
121
c)
√11
d)
1331
5.
Solve and check your solution.
a)
8
b)
-8
c)
0
d)
no solution
6.
Solve
a)
-9
b)
-2,3
c)
5
d)
0
7.
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
8.
What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)
a)
(1, 2) (3, 8) (-3, 6)
b)
(1, 2) (8, 3) (-3, 6)
c)
(-1, -2) (-3, -8) (3, -6)
d)
(2, 1) (8, 3) (6, -3)
9.
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
10.
Which is f-1(x)?
a)
f-1(x)=3∛(x-6)
b)
f-1(x)=-6+3∛x
c)
f-1(x)=∛(3x-18)
d)
f-1(x)=3(x-6)3
11.

 y=12x+5y=\frac{1}{2}x+5  

a)

 y=2x+10y=2x+10  

b)

 y=2x−10y=2x-10  

c)

 y=2x−5y=2x-5  

d)

 y=−12x−5y=-\frac{1}{2}x-5  

12.
Find the inverse 
f(x)= (x-2)5+3
a)
5√(x-3) +2
b)
-2+x5
c)
(x+1)5+3
d)
5√(x+2)-3
13.

When f(x) = 9 - 3x and g(x) = 5x - 7

find f(x) + g(x).

a)

14x - 10

b)

-8x + 2

c)

2x + 2

d)

2x - 2

14.
p(x) = 3x + 4
q(x) = 2x2
Find q(p(-2))
a)
8
b)
-8
c)
28
d)
None of these.
15.

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

16.

f(x)=2x + 4

g(x)=3x2 - 1

Find f(x) ⋅ g(x)

a)

6x4 + 12x3 - 4x2 - 8x

b)

-6x3 + 12x2 + 2x - 4

c)

6x3 + 12x2 - 2x - 4

d)

5x2 - 18x + 20

17.
f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))
a)
19
b)
23
c)
-10
d)
None of these.
18.

p(x) = 3x + 4

q(x) = 2x2

Find p(q(x))

a)

10x2

b)

18x2 + 4

c)

6x2 + 4

19.
What are the transformations of this functions compared to the parent function?
a)
Shifted down 2
b)
Shifted up 2
c)
Shifted left 2
d)
Shifted right 2
20.

What is the equation of the graph?

a)

y = √(x - 3)

b)

y = √(x) + 3

c)

y = √(x - 5) + 4

d)

y = √(x + 5) + 4

21.
Which of these equations shifts a radical equation left 3 times?
a)
y = √(x) + 3
b)
y = √(x) - 3
c)
y = √(x + 3)
d)
y = √(x - 3)
22.
Match the correct equation with the given graph.
a)
y = √(x) + 2
b)
y = √(x) - 2
c)
y = √(x + 2)
d)
y = √(x - 2)
23.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

(-∞, 0)

d)

[ 0, ∞)

24.
What are the transformations for the graph of
the parent function f(x) = √x  to the function above 
a)
Vertical Stretch by a factor of 2; translated down 5 units 
b)
Shifted right 2 units and down 5 units 
c)
Vertical stretch by a factor of 2; translated left 5 units
d)
Vertical stretch by a factor of 2; translated right one unit 
25.
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,∞)