Chapter 2: Q25. (page 94)

Graph each function. Identify the domain and range.
$g (x) = [[x - 2]]$

Short Answer

Expert verified

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

The graph of the function is shown below:

Step by step solution

Step-1 – Domain and range of the function.

The domain of the function is the set of all input values and range of the function is the set of all output values.

Step-2 – Determine the domain and range.

Consider the given function $g (x) = [[x - 2]]$

It can be observed that the domain of the function is the set of all real values because the function can take any value of x.

Here, the function is greatest integer it means it will produce only integer values.

Therefore, the range is the set of all integers.

Step-3 – Draw the table.

The symbol $[[x - 2]]$ means the greatest integer less than or equal to $x - 2$ .

For example: $[[[7.3]] = 7$ ,and $, [[- 1.5]] = - 2]$

Therefore, the required table is:

Step-4 – Graph the function.

The graph of the function is:

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Column A	Column B
the average (arithmetic mean) of three integers x, y, z and 29	30

Column A	Column B
$\frac{1}{4}$	$\frac{1}{m} - \frac{1}{4}$

Graph each function. Identify the domain and range.
$g (x) = [[x - 2]]$

Short Answer

Step by step solution

Step-1 – Domain and range of the function.

Step-2 – Determine the domain and range.

Step-3 – Draw the table.

Step-4 – Graph the function.

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Graph each function. Identify the domain and range.g(x)=[[x-2]]

Short Answer

Step by step solution

Step-1 – Domain and range of the function.

Step-2 – Determine the domain and range.

Step-3 – Draw the table.

Step-4 – Graph the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Logic and Functions

Decision Maths

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Graph each function. Identify the domain and range.
$g (x) = [[x - 2]]$