Chapter 4: Q51. (page 274)

Graph each function. State the domain and range.
$f (x) = [x]$

Short Answer

Expert verified

The domain is all real numbers and the range is all integers.

Step by step solution

Step 1. State the concept for step function.

The graph of a step function is a series of line segments. Because each part of a step function is linear, this type of function is called a piecewise-linear function. One example of a step function is the Greatest Interger Function, written as $f (x) = [x]$ , where $f (x)$ is the greatest integer not greater than $x$ .

For example, $[6.8] = 6$ , because 6 is the greatest integer that is not greater than 6.8 .

Type of Graph : disjointed line segments.

Step 2. Make a table for the given function.

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

$x$	$[x]$
0	0
0.5	0
1	1
1.5	1
2	2
2.5	2
3	3

Step 3. Plot the graph.

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

For the domain, see the $x$ -coordinate values. As the dots and circles overlap, the domain is all real numbers.

For range, see the $y$ -coordinate values. So, the range is all integers.

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Graph each function. State the domain and range.
$f (x) = [x]$

Short Answer

Step by step solution

Step 1. State the concept for step 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.f(x)=[x]

Short Answer

Step by step solution

Step 1. State the concept for step 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

Pure Maths

Probability and Statistics

Calculus

Statistics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Graph each function. State the domain and range.
$f (x) = [x]$