Linear, quadratic, cubic, reciprocal and exponential graphs: what each looks like, tables of values, plotting and y = abˣ.
What you will learn
- Match an equation to the shape of its graph
- Complete a table of values and plot a cubic or reciprocal graph
- Use y = abˣ: the y-intercept and finding a and b
Five shapes to know
Look at how x appears in the equation.
- Linear, y = 2x + 1: x to the power 1. A straight line.
- Quadratic, y = x² − 3: highest power 2. A U shape, or an upside-down U when the x² term is negative.
- Cubic, y = x³ − 4x: highest power 3. An S shape: from bottom left to top right when the x³ term is positive.
- Reciprocal, y = 4/x: x on the bottom. Two separate pieces that get closer and closer to the axes but never touch them.
- Exponential, y = 2ˣ: x is the power. Flat close to the x-axis on the left, steep on the right, and it crosses the y-axis at 1.
Here are y = x³ − 4x, y = 4/x (two pieces) and y = 2ˣ.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Five shapes to know
- Tables of values, then a smooth curve
- y = abˣ
- Try it: Spot the shapes
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Linear, Quadratic, Cubic, Reciprocal, Exponential
In this unit: Functions and graph transformations
Function notation, composite and inverse functions, the shapes of standard graphs, translations and reflections of y = f(x), and the graphs of sin, cos and tan (Higher).