Question

Which graph represents the following piecewise defined function?

Answer 1

We have the following function:
 f (x) = x if x <-2
 f (x) = - 2 if -2 <= x <1
 f (x) = x-3 if x> = 1
 We observe that the first function is a line of positive slope.
 The second function is a constant function.
 The third function is a line of positive slope that cuts the x-axis at (3, 0).
 The complete function includes the values x = -2 and x = 1.
 Therefore, the graph is the first from left to right.
 Answer:
 first from left to right

Answer 2

The graph (1) represents the following piecewise defined function

Further explanation:

Domain is a set of all the possible values of the function. The value at which the function is defined is known as domain.

Range is a set of values that the function takes.

The piecewise defined function is defined as a function that takes different values in different interval. It is defined on the sequence of intervals.

Given:

The piecewise function is,

$f\left( x \right)= \left\{ \begin{aligned}x,{\text{}}x< - 2 \hfill\\- 2,{\text{}} - 2 \leqslant x < 1 \hfill\\x - 3,{\text{}}x \geqslant 1\hfill\\\end{aligned} \right.$

Explanation:

The value of the function is $f\left( x \right) = x$ for all value of $x < - 2.$

The value of the function is $f\left( x \right) = - 2$ for all value of $- 2 \leqslant x < 1.$

The value of the function is $f\left( x \right) = x – 3$ for all value of $x \geqslant 1.$

The first function is linearly increasing for all value of x less than -2.

The second function is constant for value of x greater than 2 and less than 1.

The third function is also increasing function for the values of x greater than 1.

The graph (1) represents the following piecewise defined function.

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Functions

Keywords: range, domain, codomain, relation, function, graph, coordinates, close interval, open interval, values.