Problem 100
Question
What does it mean if a function \(f\) is increasing on an interval?
Step-by-Step Solution
Verified Answer
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.
1Step 1: Analyze the problem
Identify the type of problem and the appropriate mathematical technique to apply.
2Step 2: Apply the technique and solve
A function \(f\) is said to be increasing on an interval if, for any two numbers in that interval \(x_1 < x_2\), then \(.
3Step 3: Verify the result
Check the answer by substitution or alternative methods to confirm correctness.
Other exercises in this chapter
Problem 99
Begin by graphing the standard cubic function, \(f(x)-x^{3} .\) Then use transformations of this graph to graph the given function. $$ h(x)=-x^{3} $$
View solution Problem 99
Solve each quadratic equation by the method of your choice. $$ -x^{2}-2 x+1=0 $$
View solution Problem 100
Will help you prepare for the material covered in the next section. Let \(\left(x_{1}, y_{1}\right)=(7,2) \quad\) and \(\quad\left(x_{2}, y_{2}\right)=(1,-1) .
View solution Problem 100
Use the graph of \(f(x)=x^{2}\) to graph \(g(x)=(x+3)^{2}+1\).
View solution