The Cube Explosion
Why cubing a number makes it grow much faster than squaring.
Equation
y = x^1
Graph
Table
| x | y |
|---|---|
| -5 | -5 |
| -4 | -4 |
| -3 | -3 |
| -2 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
| 10 | 10 |
What this lesson covers
What you do
You shape the function y = x^k and watch the graph answer.
Challenges to clear
- Turn the power dial k to 3: cubes! Check 3³ = 27 in the table.
- The explosion: 5³ = 125, while squaring only reached 25.
- Turn the power dial to cubes — slide k to 3.
- There is a multiplier as well. Slide a until x = 2 reads 16: 2³ is 8, so a is 2.
Check yourself
Why does the graph of y = x^3 rise much steeper than y = x^2 for x > 2?
- Because cubing multiplies the number by itself three times, adding an extra factor of x. — correct
- Because the cube function has a higher starting point on the y-axis.
- Because squares only work for positive numbers, but cubes work for all.
- Because the graph of x^3 is a straight line, while x^2 is curved.
Think about it
- At k = 2, x = 5 gives 25. How big will x = 5 be at k = 3?