Key Features of Exponential Graphs
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.
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.
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
11 questions on Exponential Graphs — practise free
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