a Determine the piece to be used and evaluate f(- 5).
B
b Determine the piece to be used and evaluate f(2).
C
c Determine the piece to be used and evaluate f(8).
A
a Yes, it is a solution.
B
b Yes, it is a solution.
C
c No, it is not a solution.
a We are given a piecewise function and are asked to determine whether each of the given points is a solution of f(x). To do so, we will evaluate each x-value and see if the answer matches the given y-value.
f(x)=
3 &ifx<2
- x+1 &if2≤ x <6,
x &if x ≥ 6
Is ( - 5, 3) a solution of f(x)?
As - 5< 2, we will use the piece f(x)=3.
f( - 5)= 3
Since 3= 3, the point (- 5,3) is a solution of f(x).
b Is ( 2, - 1) a solution of f(x)? As 2 is greater than or equal to 2 and less than 6, we will use the piece f(x)=- x+1.
f( 2)=- 2+1 ⇔ f( 2)= - 1
Since - 1= - 1, the point (2,- 1) is a solution of f(x).
c Is ( 8, - 7) a solution of f(x)? As 8≥ 6, we will use the piece f(x)=x.
f( 8)= 8
Since - 7≠ 8, the point (8,- 7) is not a solution of f(x).
