Consider the following graph of a piecewise-defined function.
choose the correct expression to represent the piecewise defined function.
1.x< -2,f(x)=
a.-3
b.5
c.2
2.-2 a. x+2
b.2x+2
c.2x
3.x> 3,f(x)=
a.-3
b.5
c.2
.

A piecewise-defined function is one that you define not by a single equation, but by two or more. From the figure, we know that this piecewise-defined function is defined by three equations, so our goal is to find each. Two of these equations are constant functions while the other equation is a linear function. So:

1. FOR THE FIRST CONSTANT FUNCTION:

Keep in mind that for this constant function at x = 2, it isn't defined, that's why we choose the symbol <

2. FOR THE LINEAR FUNCTION:

Keep in mind that for this linear function at x = 3, it isn't defined, that's why we use the symbol <

3. FOR THE SECOND CONSTANT FUNCTION:

Keep in mind that for this constant function at x = 3, it is defined, that's why we choose the symbol ≥

In conclusion, the function is:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

correct answer is c. just did it

step-by-step explanation: