Answer the function

Question

i really do not understand how to do this at all.

f(x)={(x+1, x<-2),(5, -2<=x<=3), (x^2, x>3):}

A: Sketch the function

B: Evaluate f(5)

C: Evaluate f(3)

 

 

Answer 1

Hi Jenna:

 

You have a function that is split into 3 parts depending on the value of x.

This is called a piecewise function.

 

For all x<-2, f(x) = x+1

 

For all -2≤x≤3, f(x) = 5

 

For all x>3, f(x) = x²

 

This platform really doesn't lend itself well to graphing.

But, for any number less than -2 sketch the line  y=x+1

ending at the point (-2,-1) with an open circle at the point

(-2,-1) because the point x=-2 is not included here.

x  |  y

---|----

-5 | -4

-4 |  -3

 

 

For all numbers between -2 and 3 the line is a horizontal

line at y=5  from (-2, 5) to (3, 5)

 

For all numbers greater than 3, graph y = x²

with an open circle at the point (3, 9) because that

point is not actually included in this part of the function.

x       y

----------

4       16

5       25

 

 

 

f(5) falls in the part where x>3 so f(5) = 5² = 25

 

f(3) falls in the part where -2≤x≤3, f(x) = 5 ... so f(3) = 5

 

Questions?