WorksheetsRadical 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
(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=21x+5
a)
y=2x+10
b)
y=2x−10
c)
y=2x−5
d)
y=−21x−5
12.
Find the inverse
f(x)= (x-2)5+3
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))
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))
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
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.
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,∞)
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