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WorksheetsChapter 6: Properties of Functions
Total questions: 40
Worksheet time: 2hrs 48mins
Name
Class
Date
1.
What type of function is shown?
a)
cube root
b)
square root
c)
logarithm
d)
exponential
2.
What type of function is shown?
a)
linear
b)
quadratic
c)
square root
d)
absolute value
3.
What type of function is shown?
a)
Exponential
b)
square root
c)
quadratic
d)
cube root
4.
Describe the end behavior of the graph.
a)
x →∞, y→∞ and x→∞, y→⁻∞
b)
x →∞, y→∞ and x→⁻∞, y→∞
c)
x →∞, y→∞ and x→⁻∞, y→0
d)
x →∞,y→0 and x→∞, y→⁻∞
5.
Describe the end behavior of the graph.
a)
x → ∞, y→ ∞ and x→∞, y→⁻∞
b)
x → ∞, y→ ∞ and x→⁻∞, y→∞
c)
x → ∞, y→ ∞ and x→⁻∞, y→ 0
d)
x → ∞,y→ ∞and x→ ⁻∞, y→ ⁻∞
6.
Describe the end behavior of the graph.
a)
x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
b)
x →∞, y→∞ and x→⁻∞, y→∞
c)
x →∞, y→∞ and x→⁻∞, y→0
d)
x →∞,y→∞ and x→⁻∞, y→⁻∞
7.
Over what interval is this function constant?
a)
-5 < x < ∞
b)
-3 < x < 4
c)
4 < x < ∞
d)
-5
8.
Using the pictured graph, what is f(-3)?
a)
-3
b)
-1
c)
1
d)
3
9.
What is the range of the graph?
a)
y≥1
b)
x≥1
c)
All real numbers
d)
none of these
10.
What is the domain?
a)
-4 < x ≤ 5
b)
-4 ≤ x < 5
c)
-3 < y < 3
d)
-3 ≤ y ≤ 3
11.
Name the changes from the parent function (x2) for the following quadratic function: f(x) = 2x2 - 4
a)
Vertical stretch and translate down 4
b)
Reflection over x-axis and vertical stretch
c)
Vertical shrink and reflection over x-axis
d)
Vertical shrink and translate down 4
12.
Determine the transformation from the parent function (x) for the following linear function: f(x) = -1/2 x
a)
Translation down 2 and vertical shrink
b)
Reflection over x-axis and vertical shrink
c)
Vertical stretch and reflection over y-axis
d)
Vertical shrink only
13.
What is f(-1)?
a)
6
b)
-2
c)
sqrt(2)
d)
DNE
14.
What is the RANGE of the function?
a)
(-∞, +∞)
b)
(-∞, 4]
c)
(-∞, 4)
d)
[0, 4]
15.
Which piecewise function corresponds to this graph? (Take your time)
a)
f(x) = { x if x < 4; -x+1 if x ≥ 4
b)
f(x) = { x if x ≤ 4; -x+1 if x > 4
c)
f(x) = { -x+1 if x < 4; x if x ≥ 4
d)
f(x) = { -x+1 if x ≤ 4; x if x > 4
16.
What are the domain restrictions for the green piece of this function?
a)
-2 < x ≤ 1
b)
-1 < x ≤ 0.5
c)
x > -2
d)
x ≤ 1
17.
What is the DOMAIN of the function?
a)
(-∞, +∞)
b)
(-∞, -3) U (-3, +∞)
c)
(-∞, 2] U [3, +∞)
d)
(-∞, 3] U [3, +∞)
18.
Match the graph with the correct equation.
a)
b)
c)
d)
19.
If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?
a)
f(x - 3)
b)
f(x + 3)
c)
f(x) + 3
d)
f(x) - 3
20.
The original graph is f(x). The new graph is up 5, left 3, and reflected across the x-axis.
a)
f(x + 3) + 5
b)
-f(x - 3) + 5
c)
-f(x + 3) + 5
d)
-f(x + 5) + 3
21.
What is the equation of the graph below?
a)
f(x) = - I x + 2 I
b)
f(x) = - I x - 2 I
c)
f(x) = I x + 2 I
d)
f(x) = I x - 2 I
22.
What is the transformation?
a)
Vertical Translation up 2 and Horizontal translation right 1
b)
Vertical Translation down 2 and Horizontal Translation left 1
c)
Horizontal Translation left 2 and Vertical Translation up 1
d)
Horizontal Translation right 2 and Vertical Translation down 1
23.
The original function has equation f(x). State the transformations given the new function f(x) = ⅔(x - 7)2
a)
Vertical Shrink of ⅔
Right 7
Right 7
b)
Horizontal Shrink of ⅔
Left 7
Left 7
c)
Left ⅔
Vertical stretch of 7
Vertical stretch of 7
d)
Right ⅔
Horizontal stretch of 7
Horizontal stretch of 7
24.
Describe the transformation of y = f(x) to the new function
y = f(1/5x)
y = f(1/5x)
a)
Horizontal shrink by a factor of 1/5
b)
Vertical stretch be a factor of 5
c)
Vertically shrink by a factor of 1/5
d)
Horizontal stretch by a factor of 5
25.
Identify the transformation
a)
Vertical shrink by a factor of 2
b)
Vertical compression by a factor of 1/2
c)
Horizontal stretch by a factor of 2
d)
Horizontal compression by a factor of 1/2
26.
Given h(x)=x2+1, find 5h(x).
a)
5h(x)=5x2+5
b)
5h(x)=5x2+1
c)
5h(x)=26
d)
5h(x)=20
27.
If f(x) = 4x+8 and
g(x) = x+3,
find f(x) * g(x).
g(x) = x+3,
find f(x) * g(x).
a)
4x2+24
b)
4x2+20x+24
c)
4x2+12x+24
d)
4x2+4x+24
28.
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
29.
When f(x) = x2 -9
and g(x) = x+3 ,
find (f/g)(x).
and g(x) = x+3 ,
find (f/g)(x).
a)
x-3
b)
x+3
c)
x-12
d)
x-6
30.
a)
9 - 8/3
b)
9 + 8/3
c)
3
d)
1/3
31.
The inverse has been reflected over which line?
a)
y = x
b)
y =1
c)
y = 0
d)
y = x + 1
32.
Find the inverse of f(x) = -2/3x + 1/4
a)
f-1(x) = -3/2x + 3/8
b)
f-1(x) = 3/2x - 3/8
c)
f-1(x) = -3/2x + 8/3
d)
f-1(x) = 3/2x + 3/8
33.
Are the following inverses of each other?
a)
Yes
b)
No
34.
p(x) = 3x + 4
q(x) = 2x2
Find p(q(x))
q(x) = 2x2
Find p(q(x))
a)
10x2
b)
18x2 + 4
c)
6x2 + 4
d)
None of these
35.
f(x) = 3x + 10
g(x) = x - 2
Find f(g(x))
g(x) = x - 2
Find f(g(x))
a)
3x + 4
b)
3x - 4
c)
3x + 8
d)
None of these.
36.
f(x) = 3x
g(x) = 2x2 - 1
h(x) = 2x
Find g(f(h(x)))
g(x) = 2x2 - 1
h(x) = 2x
Find g(f(h(x)))
a)
72x2 -1
b)
18x2 -1
c)
12x2 -1
d)
144x2 -1
37.
f(x) = 3x
g(x) = 2x2 - 1
h(x) = 2x +4
Find f(g(h(2)))
g(x) = 2x2 - 1
h(x) = 2x +4
Find f(g(h(2)))
a)
21
b)
381
c)
189
d)
105
38.
What is the name of this function?
a)
Parabola
b)
Rational Function
c)
Ellipse
d)
Cubic
39.
Are the following inverses of each other?
a)
True
b)
False
40.
Was the inverse function found correctly?
a)
no,
b)
yes
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