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Identifying Exponential vs Linear Relationships

Part of Exponential Graphs — GCSE Mathematics

This deep dive covers Identifying Exponential vs Linear Relationships 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 6 of 10 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 6 of 10

Practice

11 questions

Recall

10 flashcards

Identifying Exponential vs Linear Relationships

Feature	Linear	Exponential
Differences between consecutive terms	Constant	Increasing
Ratios between consecutive terms	Varying	Constant
Graph shape	Straight line	Curved, with increasing steepness
Example sequence	5, 8, 11, 14 (add 3)	3, 6, 12, 24 (multiply by 2)

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.

Exponential Growth and Decay in Real Life Exam Tips for Exponential Graphs The Power of Doubling Exponential Graph Essentials

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.

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Exponential Growth and Decay in Real Life

Exam Tips for Exponential Graphs