Chapter 4: Q56. (page 274)

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

Short Answer

Expert verified

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

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 :

$y = f (x) = \{\begin{matrix} 2 x - 3; x \leq 2 \\ x + 1; x > 2 \end{matrix}\}$

Step 2. Make a table for the given function.

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

$x$	$x > 2$	$x \leq 2$	$y = f (x) = \{\begin{matrix} 2 x - 3; x \leq 2 \\ x + 1; x > 2 \end{matrix}\}$
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 $y = - 1$ , the range is $\{y : y > 3 or y \leq - 1\}$ .

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

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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Graph each function. State the domain and range.fx=2x−3ifx≤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

Logic and Functions

Pure Maths

Discrete Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

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