Which of the following is ALWAYS TRUE about a function f? □ If f(x) is a rational function with denominator equal to x² + 1, then f'(x) exists for all real numbers a. O f' is defined for all in the domain of f. If the tangent line at (c, f(c)) is vertical, then lim f(c+h)-f(c) h exists. h→0 If f(x) is a polynomial function, then f(x) is continuous at x = 0 and differentiable there.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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2.2 Please answer ASAP.
Which of the following is ALWAYS TRUE about a function f?
□ If f(x) is a rational function with denominator equal to x² + 1, then f'(x) exists for all real numbers x.
O f' is defined for all x in the domain of f.
If the tangent line at (c, f(c)) is vertical, then lim
f(c+h)-f(c)
h
exists.
h→0
□ If f(x) is a polynomial function, then f(x) is continuous at x = 0 and differentiable there.
Transcribed Image Text:Which of the following is ALWAYS TRUE about a function f? □ If f(x) is a rational function with denominator equal to x² + 1, then f'(x) exists for all real numbers x. O f' is defined for all x in the domain of f. If the tangent line at (c, f(c)) is vertical, then lim f(c+h)-f(c) h exists. h→0 □ If f(x) is a polynomial function, then f(x) is continuous at x = 0 and differentiable there.
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