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Exponential Graph Essentials

Part of Exponential Graphs — GCSE Mathematics

This key facts covers Exponential Graph Essentials within Exponential Graphs for GCSE Mathematics. Revise Exponential Graphs in Graphs for GCSE Mathematics with 11 exam-style questions and 10 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 2 of 10 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 10

Practice

11 questions

Recall

10 flashcards

Exponential Graph Essentials

General form: y = aˣ (where a > 0, a ≠ 1)
Growth (a > 1): curve rises steeply to the right (e.g. y = 2ˣ)
Decay (0 < a < 1): curve falls to the right (e.g. y = (0.5)ˣ)
y-intercept: always (0, 1) because a⁰ = 1 for any base a
Asymptote: y = 0 (x-axis) — the curve never touches or crosses it
y is always positive — exponential graphs are always above the x-axis

Quick Recall Flashcards

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).

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.

Exponential Graph Essentials

Exponential Graph Essentials

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Practice Questions for Exponential Graphs

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