Determine whether the following state-ments are true and give an explanation or counterexample. a) All polynomials are rational functions, but not all

Tazmin Horton 2020-12-09 Answered
Determine whether the following state-ments are true and give an explanation or counterexample.
a) All polynomials are rational functions, but not all rational functions are polynomials.
b) If f is a linear polynomial, then f×f is a quadratic polynomial.
c) If f and g are polynomials, then the degrees of f×g and g×f are equal.
d) To graph g(x)=f(x+2), shift the graph of f 2 units to the right.
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Expert Answer

Ezra Herbert
Answered 2020-12-10 Author has 99 answers
Step 1
(a) Given:
All polynomials are rational functions, but not all rational functions are polynomials.
Determine whether the following state-ments are true and give an explanation or counterexample.
Step 2
Explanation- A polynomial of degree n has at most n real zeros. The degree of a polynomial function determines the end behavior of its graph. A rational function is a function of the form f(x)=P(x)Q(x) or f(x)=P(x)Q(x), where P(x) and Q(x) are both polynomials.
Every polynomial function is a rational with Q(x)=4. A function that cannot be written in the form of a polynomial, such as , is not a rational function.
So, the given statement "All polynomials are rational functions, but not all rational functions are polynomials" is true statement.
Answer:
Hence, the given statement "All polynomials are rational functions, but not all rational functions are polynomials" is true statement.
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Jeffrey Jordon
Answered 2022-01-24 Author has 2047 answers

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