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Exponential Graphs

Revise Exponential Graphs in Graphs for GCSE Mathematics with 11 exam-style questions and 10 flashcards. This topic appears regularly enough that it should be part of a solid GCSE revision cycle.

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1

The Power of Doubling

Introduction2

Exponential Graph Essentials

Key Facts3

Exponential Growth vs Decay

Diagram4

Key Features of Exponential Graphs

Deep Dive5

Exponential Growth and Decay in Real Life

Deep Dive6

Identifying Exponential vs Linear Relationships

Deep Dive7

Exam Tips for Exponential Graphs

Exam Tips8

Worked Examples

Notes9

Common Misconceptions

Misconceptions10

Topic Summary: Exponential Graphs

Summary

Sample Flashcards

What is the asymptote of y = aˣ?
The x-axis (the line y = 0) is a horizontal asymptote. For growth (a > 1): as x → -∞, y → 0 but never reaches 0 For decay (0 < a < 1): as x → +∞, y → 0 but never reaches 0 The graph gets infinitely close to the x-axis but never crosses it. y is always positive — it never equals zero.
What is the y-intercept of any graph y = aˣ?
The y-intercept is always (0, 1). Reason: when x = 0, y = a⁰ = 1 for any base a. This is true for y = 2ˣ, y = 3ˣ, y = 5ˣ, and even y = (0.5)ˣ. All exponential graphs of the form y = aˣ pass through (0, 1).

Sample Questions

The graph of y = 3ˣ always passes through which point?

  • A. (0, 0)
  • B. (0, 1)
  • C. (1, 0)
  • D. (3, 0)
1 markfoundation

Explain why the graph of y = 3ˣ has a horizontal asymptote at y = 0, and state the domain of values that y can take.

2 markshigher

11

exam-style questions

10

revision flashcards

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