This deep dive covers Key Features of Exponential Graphs 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 4 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 4 of 10
Practice
11 questions
Recall
10 flashcards
Key Features of Exponential Graphs
The y-intercept is Always (0, 1)
For any y = aˣ, substituting x = 0 gives y = a⁰ = 1. This is true for every base — y = 2ˣ, y = 10ˣ, y = (0.5)ˣ all pass through (0, 1).
Exception: y = k × aˣ passes through (0, k) instead, because when x = 0, y = k × a⁰ = k × 1 = k.
The Asymptote y = 0
- For growth (a > 1): as x → −∞, y → 0 (curve approaches x-axis from above)
- For decay (0 < a < 1): as x → +∞, y → 0 (curve approaches x-axis from above)
- The curve NEVER crosses the x-axis — y is always positive
Comparing Growth Rate
The larger the base a, the steeper the growth curve. y = 3ˣ rises faster than y = 2ˣ. Both pass through (0, 1) and have the same asymptote y = 0, but y = 3ˣ grows much more steeply for large x values.