Parent Function and Graphs
Operations on Functions
Composite Functions
Volume
100
What is the parent function of this graph? What kind of slope does it have?
Linear; Negative slope
100
If I have functions: f(x)=3x-2; g(x)=x; h(x)=9
What is (f+g+h)(1)?
(f+g+h)(x)=(3x-2)+x+9=4x+7
(f+g+h)(1)=4(1)+7=11
100
I have two functions: j(x)=7x and m(x)=2x/3
What is (j⨀m)(9)? (Where ⨀ is the symbol for composition)
(j⨀m)(9)=j(6)=42
100
What is the volume for the shape above? (Hint: V=l*w*h)
V=144
200
What is the domain and range of this graph?
Domain is [0, infinity)
Range is [0,infinity)
200
If I have functions: f(x)=3x-2; g(x)=x/3; h(x)=9
What is (g-f)(6)?
g(6)=6/3=2
f(6)=3(3)-2=7
(g-f)(6)= 2-7= -5
200
Based on the table, what is f(g(3))?
f(g(3)) = 1
200
Frodo the dog got a ball for Christmas. If it has a radius of 3 cm, what is the volume?
V=36pi cm3 = 113.097 cm3
300
What is the parent function of this graph?
Quadratic
300
If I have functions: f(x)=3x-2; g(x)=x/3; h(x)=9
What is (f*h)(1), where * symbolizes multiplication?
(f*h)(x)=(3x-2)*(9)=27x-18
(f*h)(1)=27(1)-18=9
OR (f*h)(1)=(3(1)-2)*(9)=(1)*(9)=9
300
Based on the table, what is g(f(2))?
g(f(2)) = 1
300
What is the volume of the cone, if the radius is 2 inches and the height is 6 inches? (You may leave your answer without multiplying pi, for example, leave it as 156pi in3.)
V=8pi in3 =25.133 in3
400
What is the name of this graph's parent function?
Cubic
400
If I have functions: f(x)=3x-2; g(x)=x/3; h(x)=9
What is (g/h)(x)?
(g/h)(x)=(x/3)/9 =x/27
400
I have two functions: f(x)=3x-2 and g(x)=4x
What is the simplified form for g(f(x))?
g(f(x))=4(3x-2)=12x-8
400
Suppose I have a cup with height 7 in. and radius 3 in. that looks like this: 
What is the volume my cup can hold?
V=63pi in3 = 197.920 in3
500
Which parent function would be most appropriate for this situation:
The amount of candy received from each house on Halloween is the same. The graph shows the number of houses visited to the total amount of candy gained.
Linear
500
If I have functions: f(x)=3x-2; g(x)=x/3; h(x)=9
What is (f-h)(4)
(f-h)(4)=(10)-(9)=1
500
If I have functions: f(x)=3x-2; g(x)=x/3; h(x)=9,
What is f(g(h(1)))? (Where ⨀ is the symbol used for composition)
f(g(h(1)))=f(g(9))=f(3)=7
500
Blowing up balloons for the party, Jane had balloons with a radius of 3inches and a volume of 36pi in3. Jane's boss wants the balloons to have double the radius (6 inches). How many times bigger will the new volumes be?
New Volume: 288pi in3
288pi/36pi = 8
The balloons will be 8 times bigger.