Question

Explain how to graph the given piecewise-defined function. Be sure to specify the type of endpoint each piece of the function will have and why.
f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x + 3, 2nd column x less-than 2 2nd row 1st column 3, 2nd column 2 less-than-or-equal-to x less-than 4 3rd Row 1st column 4 minus 2 x, 2nd column x greater-than-or-equal-to 4 EndLayout

Answer 1

Answer:

Graph exists as a mathematical representation of a network and it represents the connection between lines and points.

Step-by-step explanation:

Given,

$\left\{\begin{array}{cc}-x+3 & \quad x < 2 \\ 3 & \quad 2 \leq x < 4 \\ 4-2 x & \quad x \geq 4\end{array}\right.$

Step 1

The Graph of f(x) = -x + 3 exists draw for x less than 2 because x is bounded.

The Graph of f(x) = 3 exists draw for x greater than and equal to 2 and less than 4 because x is bounded.

The Graph of f(x) = 4 - 2x exists draw for x greater than equal to 4 because x is bounded.

The graph is given below for reference.

f(x) = -x + 3 is denoted by purple.

f(x) = 3 is denoted by orange.

f(x) = 4 - 2x is denoted by green.

#SPJ3

Answer 2

Concept:

The graph is a representation of a function. A function that contains pieces of different functions in different intervals is known as a piecewise function.

Given:

A piecewise function,

f(x) = -x + 3, x < 2

f(x) = 3, 2 ≤ x< 4

f(x)= 4 - 2x, x ≥ 4

Find:

The graph of piecewise function.

Solution:

As the piecewise functions are:

f(x) = -x + 3, x < 2

f(x) = 3, 2 ≤ x< 4

f(x)= 4 - 2x, x ≥ 4

The first function must be drawn for the values of x less than 2, the second function will be drawn in between the value of x greater than or equal to 2 and less than 4. The last function will be drawn for the value of x equal to or greater than 4.

The graph is attached.

Here, the  represents the function f(x) = -x + 3,  represents the function f(x) = 3  and  represents the function f(x) = 4 - 2x.

#SPJ2