Look at the table that you completed in Part B. How does the slope change?
A
a
Graph:
B
b
Table:
x
-4
-3
-2
-1
0
1
2
3
4
f(x)
16
9
4
1
0
1
4
9
16
slope
-7
-5
-3
-1
1
3
5
7
C
c
See solution.
Practice makes perfect
a
To graph f(x)=x^2, we will make a table of values. By substituting several points for x into the function, we can have an idea about the shape of the graph. Let's start!
x
f(x)=x^2
f(x)
-3
f( -3)=( -3)^2
9
-2
f( -2)=( -2)^2
4
-1
f( -1)=( -1)^2
1
0
f( 0)=( 0)^2
0
1
f( 1)=( 1)^2
1
2
f( 2)=( 2)^2
4
3
f( 3)=( 3)^2
9
Now, we will write the ordered pairs by looking at the table.
(-3,9), (-2,4), (-1,1), (0,0)
(1,1), (2,4), (3,9)
Next, we will plot the ordered pairs and draw a smooth curve through these points.
b
Let's first complete the second row, the values of f(x). To do that, we can get help from the table in Part A.
x
-4
-3
-2
-1
0
1
2
3
4
f(x)
16
9
4
1
0
1
4
9
16
slope
-7
Let's consider how we find the slope. To find the slope, we divide the change in y by the change in x.
m=y_2-y_1/x_2-x_1
Now we will make another table to find the slope of the consecutive numbers.
Consecutive Points
m=y_2-y_1/x_2-x_1
Slope
(-4,16)-(-3,9)
m=9-16/-3-(-4)
-7
(-3,9)-(-2,4)
m=4-9/-2-(-3)
-5
(-2,4)-(-1,1)
m=1-4/-1-(-2)
-3
(-1,1)-(0,0)
m=0-1/0-(-1)
-1
(0,0)-(1,1)
m=1-0/1-0
1
(1,1)-(2,4)
m=4-1/2-1
3
(2,4)-(3,9)
m=9-4/3-2
5
(3,9)-(4,16)
m=16-9/4-3
7
Finally, we can complete the table by looking at the slope table.
x
-4
-3
-2
-1
0
1
2
3
4
f(x)
16
9
4
1
0
1
4
9
16
slope
-7
-5
-3
-1
1
3
5
7
c
We can say that the rate of change is not
constant. It decreases as x approaches 0 and then increases as x approaches infinity.
