This exam tips covers Exam Tips for 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 7 of 10 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
💡 Exam Tips for Exponential Graphs
- y-intercept is always (0, 1) for y = aˣ — mark this point first when sketching
- Curve never crosses x-axis — draw it approaching but never touching the x-axis
- Growth vs decay: growth curves rise to the right; decay curves fall to the right
- For y = k × aˣ: the y-intercept is (0, k), not (0, 1)
- Compound interest: use the formula A = P(1 + r/100)ⁿ — the multiplier is (1 + r/100) for growth, (1 − r/100) for decay
- Check if exponential: calculate the ratio of consecutive terms — if constant, it is exponential
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 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.
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).