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Flip to reveal answersWhat point does every y = aˣ pass through?
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All 9 Flashcards — Exponential functions
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Question
What point does every y = aˣ pass through?
Answer
(0, 1), because a⁰ = 1.
Question
Asymptote and range of y = aˣ?
Answer
Horizontal asymptote y = 0; range y > 0 (always positive).
Question
Growth vs decay for y = aˣ?
Answer
a > 1 grows; 0 < a < 1 decays. Both pass through (0, 1).
Question
What happens to the asymptote in y = aˣ + c?
Answer
It lifts to y = c (the curve levels off at c, not 0).
Question
y-intercept of y = k·aˣ + c?
Answer
At x = 0: k·1 + c = k + c.
Question
In a model A₀·bᵗ, what is A₀?
Answer
The initial value (at t = 0).
Question
In A₀·bᵗ, what does b tell you?
Answer
The per-period factor: b > 1 growth, b < 1 decay.
Question
How do you find when a model reaches a target?
Answer
Solve A₀·bᵗ = target with logs, or graph and use intersect on the GDC.
Question
Does y = aˣ have an x-intercept?
Answer
No — it's always positive, never reaching the x-axis.
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Full study notes for Exponential functions
Topic 2.9 hub
Exponential & log functions
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