# Exponential and Reciprocal Graphs

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Examples, solutions, and videos to help GCSE Maths students learn about exponential graphs and reciprocal graphs.

How to sketch exponential graphs and reciprocal graphs?

Exponential Functions - Introduction
y = ax, where a > 0

Sketching exponential graphs (using reflections)
Examples:
y = e-x
y = -ex

Sketching exponential graphs (using translations)
Examples:
y = ex + 2
y = ex - 1
y = ex - 2
y = ex + 1

Sketching exponential graphs (using stretches)
Examples:
y = e2x
y = ex/2
y = 2ex
y = 1/2 ex

GCSE Maths revision Exam paper practice exponential graphs
GCSE Exam paper practice question for AQA Higher Unit 3 Question 15 - exponential graphs
Example:
1000 bacteria are put into a Petri dish.
After 1 hour there are 2000 bacteria in the dish.
The bacteria continue to double in quantity every hour.
(a) Draw a fully labelled graph to show the number of bacteria in the dish for the first 4 hours.
(b) How many bacteria will be in the dish after 12 hours?

Sketching Reciprocal graphs of the form y = k/x

GCSE Maths - Sketching Cubic, Reciprocal and Exponential Graphs
brAlgebra - curves A Star Maths

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