# 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.

Maths (school) · Part 04: Graphs · Card 7 of 8 · Last updated 2026-10-19

## Analogy

The cubic is like a wave rolling through the middle. The reciprocal is like two boomerangs facing away.

## Example

**Values of y = 1/x**

x = 1: y = 1
x = 2: y = 0.5
x = 4: y = 0.25
x = -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.

## Related concepts

- [Coordinates](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-1)
- [Gradient](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-2)
- [y = mx + c](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-3)
- [Parallel and perpendicular lines](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-4)

Web page: https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-7
Study this card in the app: https://studyvisually.com/app/learn?category=maths-school&card=maths-school-part-4-concept-7