Card 1 of 20
EasyStudy card 1
Prompt
What exponents may appear in a polynomial?
Answer
Nonnegative integer exponents only.
MathChapter 13: Polynomial and Radical Functions
Flashcards
Polynomial Functions and Their Graphs Flashcards
Twenty recall-focused cards on degree, zeros, intercepts, graph behavior, extrema, and restricted intervals.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
How is a polynomial's degree determined?
Answer
Find the greatest exponent with a nonzero coefficient.
Card 3 of 20
EasyStudy card 3
Prompt
What is the degree of a nonzero constant polynomial?
Answer
Degree \(0\).
Card 4 of 20
EasyStudy card 4
Prompt
What is the maximum number of real zeros of a degree-\(n\) polynomial?
Answer
At most \(n\).
Card 5 of 20
EasyStudy card 5
Prompt
If \(f(c)=0\), what graph point is guaranteed?
Answer
The \(x\)-intercept \((c,0)\).
Card 6 of 20
EasyStudy card 6
Prompt
Are a zero and an \(x\)-intercept written the same way?
Answer
No. The zero is \(c\); the intercept is \((c,0)\).
Card 7 of 20
EasyStudy card 7
Prompt
What is the \(y\)-intercept of \(f\)?
Answer
\((0,f(0))\).
Card 8 of 20
MediumStudy card 8
Prompt
What does increasing mean on a graph?
Answer
Reading left to right, \(y\)-values rise as \(x\) rises.
Card 9 of 20
MediumStudy card 9
Prompt
What does decreasing mean on a graph?
Answer
Reading left to right, \(y\)-values fall as \(x\) rises.
Card 10 of 20
MediumStudy card 10
Prompt
What direction change identifies a local maximum?
Answer
Increasing to decreasing.
Card 11 of 20
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Prompt
What direction change identifies a local minimum?
Answer
Decreasing to increasing.
Card 12 of 20
MediumStudy card 12
Prompt
At \((-2,5)\), where does the maximum occur?
Answer
At \(x=-2\).
Card 13 of 20
MediumStudy card 13
Prompt
At \((-2,5)\), what is the maximum value?
Answer
The value is \(5\).
Card 14 of 20
MediumStudy card 14
Prompt
How do roots become linear factors?
Answer
A root \(r\) produces the factor \((x-r)\).
Card 15 of 20
MediumStudy card 15
Prompt
What factor corresponds to the root \(-4\)?
Answer
\((x+4)\).
Card 16 of 20
MediumStudy card 16
Prompt
Can a quadratic have no real \(x\)-intercepts?
Answer
Yes; degree gives a maximum, not an exact count.
Card 17 of 20
HardStudy card 17
Prompt
How do you find an absolute extremum on \([a,b]\)?
Answer
Compare endpoint values with all interior turning-point values.
Card 18 of 20
HardStudy card 18
Prompt
Why must graph scale be checked before reading an intercept?
Answer
A tick may represent more than one unit, changing the coordinate.
Card 19 of 20
HardStudy card 19
Prompt
Give one cubic with roots \(-2,1,4\).
Answer
\(f(x)=(x+2)(x-1)(x-4)\).
Card 20 of 20
HardStudy card 20
Prompt
Can a polynomial's values be negative while the function is increasing?
Answer
Yes. Increasing describes direction of change, not the sign of the outputs.
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