# The Six Parent Functions

```Transformations Day 1
The Six Parent Functions
PART I: Parent Functions and FAMILIES
What is a Parent Function:
Linear – Relations between…..
Quadratic – Vertical Motion, Path of flying objects
y  x2
yx
x
y
Absolute Value - Distance
x
Exponential – Population and Monetary Growth, Decay
y x
x
y
Square Root – Diameter of a steel cable to support
a given weight.
y  2x
x
y
y
Cubic – Volume Relations
y  x3
y x
x
y
x
y
PART II: Identifying the Family by a Table and Graphically
a. Predict the family by looking at the table of values.
b. Confirm your answer by plotting the points and observing the graph.
1.
x
-2
-1
0
1
y
.08
.4
2
10
3.
2.
4.
x
y
-2
-2
-1
0
-.25 0
1
2
.25 2
5.
x
y
-2
2
-1
4
0
1
2
4.8 5.5 6
x
y
0
0
1
-2
2
-4
3
-2
-2
8
-1
2
0
0
1
2
2
8
6.
X
Y
-3
-7
-2
-5
-1
-3
0
-1
1
1
x
y
4
0
PART III: Identifying the family by equation:
Place the following equations underneath the correct parent function:
y  2  3x
y  2 x 1
Linear
Exponential
Cubic
Absolute value
Square root
y  2 x3
y  2  3x
y  3x 2
y  2 x 3
y  2  x  3
2
y  3  2x
y  2 x  3 1
3 x
y
2
3
y   x  1  2
y  x 3  2
PART IV: Identifying the family by scenario:
Determine whether or not the following situations would be best represented a linear, exponential, or quadratic function.
1.) You are taking a road trip, and tracking how much gas you use per mile while on the highway.
2.) Over time the amount of bunnies in your back yard has been growing. The first year there were two rabbits, and
the next year there was four. As time went on the Rabbits continued to double every year.
3.) You riding your bike up a hill. For every 5 meters you go forward, you increase your height about 2 meters.
4.) You shoot a firework into the air, and you want to determine its height at the highest point.
5.) A baseball is hit out of the park, and you want to calculate the time at which it hits the ground.
6.) You buy a computer for full price, and each year, the value of the computer depreciates at a rate of 7%.
```