Card 1 of 20
EasyStudy card 1
Prompt
What is the source-supported exponential form?
Answer
\(f(x)=ab^x\), with \(a\ne0\), \(b>0\), and \(b\ne1\).
MathChapter 12: Composition, Recursion, and Exponential Functions
Flashcards
Exponential Functions and Graphs Flashcards
Twenty concise cards on exponential parameters, growth and decay, exact graph points, tables, domain, range, and model comparisons.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
In \(f(x)=ab^x\), what is \(f(0)\)?
Answer
\(a\), because \(b^0=1\).
Card 3 of 20
EasyStudy card 3
Prompt
What is the vertical-axis intercept of \(ab^x\)?
Answer
\((0,a)\).
Card 4 of 20
EasyStudy card 4
Prompt
Which parameter is the one-step multiplier?
Answer
The base \(b\).
Card 5 of 20
EasyStudy card 5
Prompt
When does the source classify \(ab^x\) as growth?
Answer
When \(b>1\).
Card 6 of 20
EasyStudy card 6
Prompt
When does it classify \(ab^x\) as decay?
Answer
When \(0<b<1\).
Card 7 of 20
EasyStudy card 7
Prompt
Does a positive value of \(a\) by itself mean growth?
Answer
No. Growth or decay is determined by the base \(b\).
Card 8 of 20
MediumStudy card 8
Prompt
For the positive-scale source cases, what is the domain?
Answer
All real numbers.
Card 9 of 20
MediumStudy card 9
Prompt
For the positive-scale source cases, what is the range?
Answer
The positive real numbers.
Card 10 of 20
MediumStudy card 10
Prompt
What pattern in a table suggests an exponential model?
Answer
A constant ratio between consecutive outputs for equal input steps.
Card 11 of 20
MediumStudy card 11
Prompt
What pattern suggests a linear model instead?
Answer
A constant additive difference.
Card 12 of 20
MediumStudy card 12
Prompt
How should an accurate exponential graph be built?
Answer
Equation to exact values to plotted points to curve.
Card 13 of 20
MediumStudy card 13
Prompt
Why is hand-sketching a curve before choosing a model risky?
Answer
The sketch may imply values or an intercept that do not satisfy the equation.
Card 14 of 20
MediumStudy card 14
Prompt
What is average rate of change on \([u,v]\)?
Answer
\(\frac{f(v)-f(u)}{v-u}\).
Card 15 of 20
MediumStudy card 15
Prompt
Is average rate of change the same as the exponential base?
Answer
No. One is an interval-based additive average; the other is a one-step multiplier.
Card 16 of 20
MediumStudy card 16
Prompt
What must you check before comparing two curves visually?
Answer
Their axis scales and exact values at common inputs.
Card 17 of 20
HardStudy card 17
Prompt
For \(q(x)=9(1.4)^x\), identify \(a\) and \(b\).
Answer
\(a=9\) and \(b=1.4\).
Card 18 of 20
HardStudy card 18
Prompt
For \(h(x)=32(0.75)^x\), what percent is retained per step?
Answer
\(75\%\); the model decays by \(25\%\).
Card 19 of 20
HardStudy card 19
Prompt
If \(f(0)=6\) and each output is twice the preceding output, what model fits?
Answer
\(f(x)=6(2)^x\).
Card 20 of 20
HardStudy card 20
Prompt
Why can a lower-starting growth model overtake another?
Answer
A larger repeated multiplier can eventually outweigh a smaller initial value.
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