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Chapter 2: Problem 100

What does it mean if a function \(f\) is increasing on an interval?

Short Answer

Expert verified
A function \(f\) is said to be increasing on an interval if, for any two numbers in that interval \(x_1 < x_2\), then \(f(x_1) \leq f(x_2)\). The function's value doesn't decrease as we move from left to right within the interval.

Step by step solution

01

Definition of an Increasing Function

A function \(f(x)\) is said to be increasing on an interval if, for any two numbers \(x_1\) and \(x_2\) in the interval with \(x_1 < x_2\), we have \(f(x_1) \leq f(x_2) \). This implies that the value of the function at a higher input is always at least as much as at any lower input within the interval.

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Most popular questions from this chapter

What must be done to a function's equation so that its graph is shifted vertically upward?

Begin by graphing the cube root function, \(f(x)-\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$ h(x)--\sqrt[3]{x+2} $$

Begin by graphing the cube root function, \(f(x)-\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$ h(x)--\sqrt[3]{x-2} $$

If \(f(x)=3 x\) and \(g(x)=x+5,\) find \((f \circ g)^{-1}(x)\) and \(\left(g^{-1} \circ f^{-1}\right)(x)\)

Begin by graphing the standard cubic function, \(f(x)-x^{3} .\) Then use transformations of this graph to graph the given function. $$ h(x)-\frac 1 2(x-2)^{3}-1 $$
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