Domain
Range
Composition
Transformations
Inverse Functions
100
f(x)=1/(x+1)+3
All real numbers except x=-1
100
f(x)=1/(x+1)+3
All real numbers except y=3
100
Find f(g(x)). F(x)=5x^2 G(x)=3x
45x^2
100
Describe the following transformation of y=x^2. f(x)=2(x-2)^2+5
Right 2, up 5, stretch vertically by a factor of 2
100
Are these two functions inverses of each other? f(x)=2x-7 g(x)=x/2+7/2
Yes
200
y=5x-1
All real numbers.
200
y=5x-1
All real numbers
200
Find g(f(x)). F(x)=5x^2 G(x)=3x
15x^2
200
Describe the following transformation of y=x^2. f(x)=-(x+1)^2-2
Left 1 unit, down 2 units, reflected over the y-axis
200
Are these two functions inverses of each other? f(x)=x+4 g(x)=(x-3)/2
No
300
sqrt(x-4)
x>_2
300
sqrt(x-4)
y>_0
300
Find f(g(x)). F(x)=1/x G(x)=x^2+1
1/(x^2+1)
300
Give the equation of the transformation of sqrt(x). Up 2, right 10 units, compressed vertically by a factor of 1/2.
.5sqrt(x-10)+2
300
Are these two functions inverses of each other? f(x)=sqrt(x-2) g(x)=2x^2
NO
400
f(x)=1/(2-sqrt(x))
All real numbers except x=4
400
f(x)=1/(2-sqrt(x))
All real numbers except y=4
400
Find g(f(x)). F(x)=1/x G(x)=x^2+1
(1/x^2)+1
400
Give the equation of the transformation of x^3. Down 1, left 1 units, stretched horizontally by a factor of 3.
(3x+1)^3-1
400
State the inverse operation. Raise to the 1/7th power.
Raise to 7th power
500
f(x)=5-sqrt(x^2-25)
x>_5, x<_-5
500
f(x)=5-sqrt(x^2-25)
y<_5
500
Express y as a composition of two simpler functions.
y=1+2(x-1)+5(x-1)^2
500
Draw a graph of y=2(x-3)^2-4
PICTURE
500
State the inverse operation. Multiply by 77 and add 10.
Subtract 10, divide by 77
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