Continuity on a Closed Interval In Exercises 37-40, discuss the continuity of the function on the closed interval. Function Interval f ( x ) = { 3 − x , x ≤ 0 3 + 1 2 x , x > 0 [ − 1 , 4 ]
Continuity on a Closed Interval In Exercises 37-40, discuss the continuity of the function on the closed interval. Function Interval f ( x ) = { 3 − x , x ≤ 0 3 + 1 2 x , x > 0 [ − 1 , 4 ]
Solution Summary: The author explains that all polynomials are continuous over given intervals except at point x=0, where the function has splits.
Prove or disprove: (a) A continuous function is an open function. (b) An open function is a continuous function. (c) A continuous function is a closed function. (d) A closed function is a continuous function. (e) An open function is a closed function. (f) A closed function is an open function
Consider the function f ( x ) = | x − 5 | + | x + 7 | .
(a) Write the function f ( x ) as a piece-wise defined function, where the pieces are linear functions.(That is, write f ( x ) using cases, as in Example 4 on page 6, but without using absolute values.)
(b) Use part (a) to sketch the graph of the function (by hand).
Consider the graphs of f(x ) and g (x ). For each function resulting from the operation, decide whether the resulting function is even, odd, or neither even nor odd.
a)f(x )+ g(x)
b)f(x )- g(x)
c)f(x ) x g(x)
d) f(x) / g(x)
Chapter 2 Solutions
Bundle: Calculus: Early Transcendental Functions, Loose-leaf Version, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus: Early Transcendental Functions, 6th Edition, Multi-Term
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