Cubic and reciprocal graphs
A cubic graph, such as y = x^3, is an S-shape. A reciprocal graph, y = 1/x, has two separate curves that approach the axes without touching.
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Analogy
The cubic is like a wave rolling through the middle. The reciprocal is like two boomerangs facing away.
Example
x = 1: y = 1x = 2: y = 0.5x = 4: y = 0.25x = -2: y = -0.5
In practice
Reciprocal graphs show how speed and time trade off: double the speed, half the time.
Practice
Flashcards
- What does the graph of y = 1/x look like?Two separate curves that never touch the axes.
Questions people ask
Why does y = 1/x never touch the axes?
You cannot divide by zero, so x = 0 has no answer. Also, 1 divided by any number is never exactly zero. The curve gets closer and closer to the axes but never reaches them. The axes are called asymptotes.
What does a cubic graph look like?
A basic cubic such as y = x^3 passes through the origin and rises to the right while falling to the left, forming an S-like shape. Negative x values give negative y values, because a negative number cubed stays negative.