Question

Graph the following function. Check your result using a graphing calculator.
x+1, for xs -5,
-3, for -5 f(x)=
1
3*, for x26
Choose the correct graph below.
ОА.
ОВ.
Oc.
OD.
AY
Ау
NIE

Answer 1

A piece-wise function represents functions of various intervals.

The graph of the piece-wise function is graph (b)

The piece-wise function is given as:

$f(x) = \left[\begin{array}{ccc}x + 1&x \le -5 \\-3& -5 <x<6\\\frac 13 x&x \ge 6\end{array}\right$

To plot the graph, we simply analyze each equation

$f(x) = x + 1, \ x \le-5$

$x \le-5$ means that:

• The maximum value of x for this function is -5
• The above statement means that, the graph of f(x) = x  + 1 would use a closed circle

$f(x) = -3,\ -5 < x < 6$

$-5 < x < 6$ means that

• -5 and -6 are not inclusive of the value of x
• The above statement means that the graph of f(x) in this interval would be open circle

$f(x) = \frac 13x,\ x \ge 6$

$x \ge 6$ means that

• 6 is inclusive of the value of x
• The above statement means that the graph of f(x) in this interval would be a close circle

The graph that satisfies the above conditions is: graph (b)

Read more about graphs of piece-wise function at:

https://brainly.com/question/12650500