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Chapter 3: Q. 6 (page 136)

True or False The graph of the function $f (x) = x^{2}$ is increasing on the interval $(0, \infty) .$

Short Answer

Expert verified

$f (x) = x^{2}$ is increasing on the interval $(0, \infty) .$

Step by step solution

01

Step 1. Given Information

Given that $f (x) = x^{2} .$

02

Step 2. Solution

Here, $f (x) = x^{2} .$

So, the graph of given function is-

This is clear in the graph that function is increasing in interval $(0, \infty) .$

03

Step 3. Final Answer

Hence, Function is Increasing in the interval $(0, \infty) .$

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Most popular questions from this chapter

True or False If the average rate of change of a linear function is $\frac{2}{3}$ , then if $y$ increases by $3$ , $x$ will increase by $2$ .

Find an equation of the line containing the points $(1, 4)$ and $(3, 8)$ .

What is the domain of the function $f (x) = \sqrt{x - 3 x^{2}}$ ?

Graph the function $f$ by starting with the graph of $y = x^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write $f$ in the form $f (x) = a (x - h)^{2} + k$ .

$f (x) = 3 x^{2} + 6 x$

True or False The graph of $f (x) = 2 x^{2} + 3 x - 4$ opens up.

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