In these lessons, we will learn
Example:
Draw the graph of y = x^{3} + 3 for –3 ≤ x ≤ 3. Use your graph to find
a) the value of y when x = 2.5
b) the value of x when y = –15
Solution:
x |
–3 |
–2 |
–1 |
0 |
1 |
2 |
3 |
y |
–24 |
–5 |
2 |
3 |
4 |
11 |
30 |
a) When x = 2.5, y 18.6
b) When y = –15, x –2.6
Example:
Plot the graph of y = x^{3} – 9x + 5 for –4 ≤ x ≤ 4 and use your graph to find:
a) the value of y when x = 1.6
b) the value of x when y = 12
Solution:
x |
–4 |
–3 |
–2 |
–1 |
0 |
1 |
2 |
3 |
4 |
y |
–23 |
5 |
15 |
13 |
5 |
–3 |
–5 |
5 |
33 |
a) When x = 1.6, y –5.3
b) When y = 12, x –0.8, or x –2.5
This video provides and example of how to graph a cubic or degree 3 polynomial function by completing a table of values.
We can graph cubic functions by transforming the basic cubic graph. The basic cubic graph is y = x^{3}.
For the function of the form y = a(x − h)^{3} + k.
If k > 0, the graph shifts k units up; if k < 0, the graph shifts k units down.
If h > 0, the graph shifts h units to the right; if h < 0, the graph shifts h units left.
If a < 0, the graph is flipped.
The following video shows how to graph cubic functions by writing the function in the form y = a(x − h)^{3} + k.