Functions and Graphs
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1. Evaluate the difference quotient for the given function. Simplify your answer.
(1) f(x)=x^3, f(3+h) - f(3)/h
2. Find the domain and sketch the graph of the given functions:
a. F(x) = 1/2 (x+3)
b. f(x) = {-1 if x< or equal to -1
3x+2 if abs(x)< 1
7-2x if x > or equal to 1
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Solution Summary
This solution is comprised of detailed explanation and graphical representation of the given function and provides students with a clear perspective of the underlying concepts of domain, difference quotient, etc.
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f(x) = x3
f(3+h) = (3+h)3 = 33+h3+3×3×h (3+h) = 27+ h3+9h(3+h) = 27+ h3+27h+9h2
f(3) = 33
f(3)/h = 33/h = 27/h
Therefore, f(3+h) - f(3)/h = 27+ h3+27h+9h2 - 27/h = ...
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