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Chapter 2: Q 1. (page 100)

Sketch the graph of $y = \sqrt{x}$

Short Answer

Expert verified

The graph of $y = \sqrt{x}$ is:

Step by step solution

01

Step 1. Given information

The given function is

$y = \sqrt{x}$

02

Step 2. Find the intercepts

Consider $y = 0$ to find the $x$ intercept

$\begin{array}{l} y = \sqrt{x} \\ 0 = \sqrt{x} \\ x = 0 \end{array}$

The $x$ intercept is $(0, 0)$

Consider $x = 0$ to find the $y$ intercept

$\begin{array}{l} y = \sqrt{0} \\ y = 0 \end{array}$

$y$ intercept is $(0, 0)$

Therefore $(0, 0)$ is the only intercept.

03

Step 3. Form the table

Substitute the values of $x, y$ to obtain the points.

x	y	(x,y)
0	0	(0,0)
1	1	(1,1)
4	2	(4,2)

04

Step 4. Plot the graph

The graph is:

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Most popular questions from this chapter

If $x = - 2$ , the value of the expression $3 x^{2} - 5 x + \frac{1}{x}$ is _______.

Determine whether each relation represents a function. For each function, state the domain and range.

$\{(- 1, 0), (2, 3), (4, 0)\}$

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$f (x) = x^{2} + 4$

In Problems 7–18, match each graph to one of the following functions:

$A . y = x^{2} + 2 B . y = - x^{2} + 2 C . y = |x| + 2 D . y = - |x| + 2 E . y = {(x - 2)}^{2} F . y = - {(x + 2)}^{2} G . y = |x - 2| H . y = - |x + 2| I . y = 2 x^{2} J . y = - 2 x^{2} K . y = 2 |x| L . y = - 2 |x|$

True or False

The graph of $y = - f (x)$ is the reflection about the $x$ -axis of the graph of $y = f (x)$ .

See all solutions

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