Substitute integers for x in the function and evaluate.
B
b
Substitute integers for x in the function and evaluate.
C
c
Substitute integers for x in the function and evaluate.
D
d
A family of function are functions that display the same characteristics — for example, linear functions which are all straight lines, and quadratic functions which are all parabolas.
A
a
Table:
x
y
- 2
- 9
- 1
0
0
1
1
2
2
3
Graph:
B
b
Table:
x
y
- 2
9
- 1
0
0
1
1
0
2
9
Graph:
C
c
Table:
x
y
- 2
0
- 1
3
0
0
1
- 3
2
0
Graph:
D
d
Part A → y=x^3
Part B → y=x^4
Part C → y=x^3
Practice makes perfect
a
Let's calculate the corresponding y-values for the given x-values. Notice that we will only be substituting integers for x.
c|c|c
x & (x-1)^2(x+1) & y [0.2em]
[-0.6em]
- 2 & ( - 2-1)^2( - 2+1) & - 9 [0.4em]
[-0.6em]
- 1 & ( - 1-1)^2( - 1+1) & 0 [0.4em]
[-0.6em]
0 & ( 0-1)^2( 0+1) & 1 [0.4em]
[-0.6em]
1 & ( 1-1)^2( 1+1) & 0 [0.4em]
[-0.6em]
2 & ( 2-1)^2( 2+1) & 3Now we can make the value table.
x
y
- 2
- 9
- 1
0
0
1
1
0
2
3
Finally, we will place the points in a coordinate plane and draw the graph.
b
Let's calculate the corresponding y-values for the given x-values. Notice that we will only be substituting integers for x.
c|c|c
x & (x-1)^2(x+1)^2 & y [0.2em]
[-0.6em]
- 2 & ( - 2-1)^2( - 2+1)^2 & 9 [0.4em]
[-0.6em]
- 1 & ( - 1-1)^2( - 1+1)^2 & 0 [0.4em]
[-0.6em]
0 & ( 0-1)^2( 0+1)^2 & 1 [0.4em]
[-0.6em]
1 & ( 1-1)^2( 1+1)^2 & 0 [0.4em]
[-0.6em]
2 & ( 2-1)^2( 2+1)^2 & 9Now we can make the value table.
x
y
- 2
9
- 1
0
0
1
1
0
2
9
Finally, we will place the points in a coordinate plane and draw the graph.
c
Let's calculate the corresponding y-values for the given x-values. Notice that we will only be substituting integers for x.
c|c|c
x & x^3-4x& y [0.2em]
[-0.6em]
- 2 & ( - 2)^3-4( - 2) & 0 [0.4em]
[-0.6em]
- 1 & ( - 1)^3-4( - 1) & 3 [0.4em]
[-0.6em]
0 & ( - 1)^3-4( 0) & 0 [0.4em]
[-0.6em]
1 & 1^3-4( 1) & - 3 [0.4em]
[-0.6em]
2 & 2^3-4( 2) & 0 [0.4em]Now we can make the value table.
x
y
- 2
0
- 1
3
0
0
1
- 3
2
0
Finally, we will place the points in a coordinate plane and draw the graph.
d
A parent function is the most basic of functions within the same family of functions. Let's list a few parent functions for some family of functions.
Family of functions
Parent function
Linear
y=x^()
Quadratic
y=x^2
Cubic
y=x^3
The function from Part C is a cubic function. Therefore, we can immediately identify its parent function.
c. y=x^3-4x → y=x^3
In order to determine the parent function for the remaining equations, we should first rewrite them so that we may identify their family.
The function from Part A is a cubic function. With this information we can identify its parent function.
a. y=(x-1)^2(x+1) → y=x^3
Let's also determine the parent functions for the equation from Part B.
As we can see, the function from Part B is a fourth degree function. With this information, we can identify its parent function.
b. y=(x-1)^2(x+1)^2 → y=x^4
