GraphsKey Facts

Exponential Graph Essentials

Part of Exponential Graphs · GCSE GCSE Mathematics revision

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

Keep building this topic

Read this section alongside the surrounding pages in Exponential Graphs. That gives you the full topic sequence instead of a single isolated revision point.

The Power of Doubling Exponential Growth vs Decay Key Features of Exponential Graphs Exponential Growth and Decay in Real Life

Practice Questions for Exponential Graphs

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

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.

11 questions on Exponential Graphs — practise free

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The Power of Doubling

Exponential Growth vs Decay