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.
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) |
Practice questions for Exponential Graphs
The graph of y = 3ˣ always passes through which point?
Explain why the graph of y = 3ˣ has a horizontal asymptote at y = 0, and state the domain of values that y can take.
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.