Exponential & log functions
Practice Flashcards
What point does every y = aˣ pass through?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All Flashcards in Topic 2.9
Below are all 18 flashcards for this topic. Sign up free to track your progress and get personalized review schedules.
2.9.19 cards
What point does every y = aˣ pass through?
(0, 1), because a⁰ = 1.
Asymptote and range of y = aˣ?
Horizontal asymptote y = 0; range y > 0 (always positive).
Growth vs decay for y = aˣ?
a > 1 grows; 0 < a < 1 decays. Both pass through (0, 1).
What happens to the asymptote in y = aˣ + c?
It lifts to y = c (the curve levels off at c, not 0).
y-intercept of y = k·aˣ + c?
At x = 0: k·1 + c = k + c.
In a model A₀·bᵗ, what is A₀?
The initial value (at t = 0).
In A₀·bᵗ, what does b tell you?
The per-period factor: b > 1 growth, b < 1 decay.
How do you find when a model reaches a target?
Solve A₀·bᵗ = target with logs, or graph and use intersect on the GDC.
Does y = aˣ have an x-intercept?
No — it's always positive, never reaching the x-axis.
2.9.29 cards
What point does y = logₐx pass through?
(1, 0), because logₐ1 = 0.
Asymptote and domain of y = logₐx?
Vertical asymptote x = 0; domain x > 0.
y = logₐx is the inverse of what?
y = aˣ — they're reflections in y = x.
Range of y = logₐx?
All real numbers (y ∈ ℝ).
Why is there no y-intercept for y = log x?
x = 0 isn't in the domain (log 0 is undefined).
Does y = log x have a horizontal asymptote?
No — it keeps increasing (slowly) forever.
Vertical asymptote of y = logₐ(x − h)?
x = h (the inside must be positive: x > h).
Domain of y = log(x − 2)?
x > 2.
How do the features of aˣ and logₐx relate?
They swap (inverses): (0,1)↔(1,0), asymptote y=0↔x=0, domains/ranges swap.
Topic 2.9 study notes
Full notes & explanations for Exponential & log functions
Math AA SL exam skills
Paper structures, command terms & tips
Want smart review reminders?
Sign up free to track your progress. Our spaced repetition algorithm will tell you exactly which cards to review and when.
Start Free