SOLUTION: The function f is defined as follows.
f(x)={x+6 if -5<=x<1}
{9 if x=1}
{-x+4 if x>1}
A.) Find the domain of the function
B.)Locate any intercepts
C.)Graph the fun
Algebra ->
Rational-functions
-> SOLUTION: The function f is defined as follows.
f(x)={x+6 if -5<=x<1}
{9 if x=1}
{-x+4 if x>1}
A.) Find the domain of the function
B.)Locate any intercepts
C.)Graph the fun
Log On
Question 1001253: The function f is defined as follows.
f(x)={x+6 if -5<=x<1}
{9 if x=1}
{-x+4 if x>1}
A.) Find the domain of the function
B.)Locate any intercepts
C.)Graph the function
The smallest x allowed is x = -5 (from the first piece of the piecewise function)
There is no limit on the upper bound of x
So the domain in interval notation is [-5, infinity)
--------------------------------------------------------------------------------------------
B)
Set each piece equal to 0 and solve for x
Piece 1:
x+6 = 0
x = -6
But x = -6 is outside of the domain. So this is not a proper intercept
Piece 2:
9 = 0 ... which is always false
Piece 3:
-x+4 = 0
-x = -4
x = 4
So the only x intercept is the ordered pair/point (4,0)
C)
To graph this piecewise function, you simply graph y = x+6, y = 9 and y = -x+4 but you apply the proper restrictions.
The graph of the piecewise function is shown below
Notice how the red piece is the piece x+6 and it is only graphed from x = -5 to x = 1. There is a closed circle at x = -5 and an open circle at x = 1. The closed circle means "include this point" while the open circle means "exclude this point"
There is a single solitary point at (1,9). This represents the middle piece "f(x) = 9 if x = 1"
Finally, the last piece is -x+4 and is it the piece in green. It has an open circle at the endpoint and stretches on forever the more x increases.
(
