SOLUTION: Given f(x) = 3x + 5x^2 − 2 − x^3 do each of the following:
A) Write it in standard form.
B) State its degree
C) Identify the type (even/odd)
D) What is the leading coeffi
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-> SOLUTION: Given f(x) = 3x + 5x^2 − 2 − x^3 do each of the following:
A) Write it in standard form.
B) State its degree
C) Identify the type (even/odd)
D) What is the leading coeffi
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Question 1154824: Given f(x) = 3x + 5x^2 − 2 − x^3 do each of the following:
A) Write it in standard form.
B) State its degree
C) Identify the type (even/odd)
D) What is the leading coefficient?
E) How many roots are there?
F) Describe the end behaviors x→ -∞, f(x)→_______ and as x→∞, f(x)→ _______ Found 2 solutions by greenestamps, MathLover1:Answer by greenestamps(13200) (Show Source):
A) Rewrite the polynomial in standard form -- i.e., in descending powers of the variable.
B) The degree of the polynomial is the degree of the leading term: 3
C) The polynomial has terms of both even and odd degrees; the polynomial as a whole is neither even nor odd.
D) The leading coefficient is the coefficient of the leading term: -1
E) The number of roots is the degree of the polynomial: 3
F) The end behavior is determined by the degree of the polynomial and the sign of the leading coefficient. Odd degree and negative leading coefficient means the value goes to +infinity as x goes to -infinity, and to -infinity as x goes to +infinity.
A) Write it in standard form.
A cubic function has the standard form of
B) State its degree
degree
C) Identify the type (even/odd)
I'll plug in for , and simplify to check if this function is even:
I can see, by a quick comparison, that this does not match what I'd started with, so this function is not even.
What about odd?
This doesn't match what I came up with, either. So the original function isn't odd, either.
=> is neither even nor odd
D) What is the leading coefficient?
the leading coefficient is
E) How many roots are there?
there are roots
F) Describe the end behaviors
Cubic functions are functions with a degree of 3 (hence cubic ), which is odd. Linear functions and functions with odd degrees have opposite end behaviors.
, and as ,
