Practice Flashcards
Flip to reveal answersWhat point does y = logₐx pass through?
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All 9 Flashcards — Logarithmic functions
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Question
What point does y = logₐx pass through?
Answer
(1, 0), because logₐ1 = 0.
Question
Asymptote and domain of y = logₐx?
Answer
Vertical asymptote x = 0; domain x > 0.
Question
y = logₐx is the inverse of what?
Answer
y = aˣ — they're reflections in y = x.
Question
Range of y = logₐx?
Answer
All real numbers (y ∈ ℝ).
Question
Why is there no y-intercept for y = log x?
Answer
x = 0 isn't in the domain (log 0 is undefined).
Question
Does y = log x have a horizontal asymptote?
Answer
No — it keeps increasing (slowly) forever.
Question
Vertical asymptote of y = logₐ(x − h)?
Answer
x = h (the inside must be positive: x > h).
Question
Domain of y = log(x − 2)?
Answer
x > 2.
Question
How do the features of aˣ and logₐx relate?
Answer
They swap (inverses): (0,1)↔(1,0), asymptote y=0↔x=0, domains/ranges swap.
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Full study notes for Logarithmic functions
Topic 2.9 hub
Exponential & log functions
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