Q56. Graph each function. State the d... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 4: Q56. (page 274)

Graph each function. State the domain and range.
$f (x) = \{\begin{array}{l} 2 x 鈭� 3 if x 鈮� 2 \\ x + 1 if x > 2 \end{array}\}$

Short Answer

Expert verified

The domain is all real numbers and the range is ${y : y > 3 or y 鈮� 1}$ .

Step by step solution

Step 1. State the concept for the given function.

This is a piece-wise defined function. Check for different values in the domain and include the values for which the function changes :

$y = f (x) = \{\begin{matrix} 2 x 鈭� 3; x 鈮� 2 \\ x + 1; x > 2 \end{matrix}\}$

Step 2. Make a table for the given function.

Construct a table for $f (x)$ by taking some values of $x$ .

$x$	$x > 2$	$x 鈮� 2$	$y = f (x) = \{\begin{matrix} 2 x 鈭� 3; x 鈮� 2 \\ x + 1; x > 2 \end{matrix}\}$
0	No	Yes	$- 3$
1	No	Yes	$- 1$
2	No	Yes	1
3	Yes	No	4
4	Yes	No	5

Step 3. Plot the graph.

Plot the values of $x$ and $f (x)$ on a graph,

The $x$ -coordinate values specify the domain of the function. Since the graph covers all possible values of $x$ , the domain is all real numbers.

The $y$ -coordinate values specify the range of the function. Since, the graph does not take any value less than or equal to $y = 3$ and more than $y = 鈭� 1$ , the range is $\{y : y > 3 or y 鈮� 鈭� 1\}$ .

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91影视

Graph each function. State the domain and range.
$f (x) = \{\begin{array}{l} 2 x 鈭� 3 if x 鈮� 2 \\ x + 1 if x > 2 \end{array}\}$

Short Answer

Step by step solution

Step 1. State the concept for the given function.

Step 2. Make a table for the given function.

Step 3. Plot the graph.

One App. One Place for Learning.

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91影视

Graph each function. State the domain and range.fx=2x鈭�3ifx鈮�2x+1ifx>2

Short Answer

Step by step solution

Step 1. State the concept for the given function.

Step 2. Make a table for the given function.

Step 3. Plot the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Pure Maths

Calculus

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Graph each function. State the domain and range.
$f (x) = \{\begin{array}{l} 2 x 鈭� 3 if x 鈮� 2 \\ x + 1 if x > 2 \end{array}\}$