Chapter 2: Q. 69 (page 103)

Define some functions that pass through $(0, 0)$ and $(1, 1)$ and are increasing for role="math" localid="1645858417003" $x \geq 0$ . Begin your list with $y = \sqrt{x}, y = x$ , and $y = x^{2}$ . Can you propose a general result about such functions?

Short Answer

Expert verified

All functions of the form $y = x^{k}$ , $k > 0$ passes through the points $(0, 0)$ and $(1, 1)$ and are increasing for role="math" localid="1645858424725" $x \geq 0$ . As the exponent $k$ increases the steepness of the curve increases.

Step by step solution

Step 1. Define the functions

The general function rule for the functions passing through the points $(0, 0)$ and $(1, 1)$ and are increasing for $x \geq 0$ is given as $y = x^{k}$ where $k > 0$ .

Some such functions are

$y = \sqrt{x} y = x y = x^{2} y = x^{3}$

and so on.

Step 2. General result

For the function $y = x^{k}$ , $k > 0$ as the exponent $k$ increases the steepness of the curve also increases.

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Define some functions that pass through $(0, 0)$ and $(1, 1)$ and are increasing for role="math" localid="1645858417003" $x \geq 0$ . Begin your list with $y = \sqrt{x}, y = x$ , and $y = x^{2}$ . Can you propose a general result about such functions?

Short Answer

Step by step solution

Step 1. Define the functions

Step 2. General result

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Define some functions that pass through (0,0)and (1,1)and are increasing for role="math" localid="1645858417003" x≥0. Begin your list with y=x,y=x, and y=x2. Can you propose a general result about such functions?

Short Answer

Step by step solution

Step 1. Define the functions

Step 2. General result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Statistics

Calculus

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Define some functions that pass through $(0, 0)$ and $(1, 1)$ and are increasing for role="math" localid="1645858417003" $x \geq 0$ . Begin your list with $y = \sqrt{x}, y = x$ , and $y = x^{2}$ . Can you propose a general result about such functions?