Evaluating
Functions
Evaluating functions means finding the value of
the function.
To evaluate 𝑓(𝑥) at 𝑥 = 𝑎, simply substitute 𝑎
for 𝑥 then simplify.
Given the function 𝑓 𝑥 = 3𝑥 + 1, find the following:
a.) 𝑓(𝟏)
b.) 𝑓(−2)
𝑓 𝑥 = 3𝑥 + 1
𝑓 𝟏 =3 𝟏 +1
𝑓 𝟏 =3+1
𝑓 𝑥 = 3𝑥 + 1
𝑓 −𝟐 = 3 −𝟐 + 1
𝑓 −𝟐 = -6 + 1
𝑓 1 =4
𝑓 −2 = −5
2
Given the function 𝑓 𝑥 = 2𝑥 − 𝑥 + 1, find the
following:
a.) 𝑓(−𝟑)
2
𝑓 𝑥 = 2𝑥 − 𝑥 + 1
b.) 𝑓(2)
𝑓 𝑥 = 2𝑥 2 − 𝑥 + 1
2
𝑓
𝟐
=
2
𝟐
−2+1
𝑓 −𝟑 = 2 −𝟑 − −𝟑 + 1
𝑓 𝟐 = 2(4) - 2 + 1
𝑓 −𝟑 = 2(9) + 3 + 1
2
𝑓 −3 = 22
𝑓 2 =7
Evaluating
PiecewiseFunc
tions
What is a piecewise function?
This is a function defined by more than one subfunctions where each sub-function has a particular
domain.
Given the above piecewise function, find the following:
a.) 𝑔(𝟏)
𝑔 𝑥 = 𝑥 2 + 8𝑥 − 1
b.) 𝑔(−𝟐)
𝑔 𝟏 = 𝟏 2+8 𝟏 −1
𝑔 𝟏 = 1+8-1
c.) 𝑔(−𝟑)
𝑔 1 =8
Given the above piecewise function, find the following:
𝑔 𝑥 = −10
b.) 𝑔(−𝟐)
𝑔 −𝟐 = −10
Given the above piecewise function, find the following:
𝑔 𝑥 = (𝑥 + 4)³
c.) 𝑔(−𝟑)
𝑔 −𝟑 = (−𝟑 + 4)³
𝑔 −𝟑 = (1)³
𝑔 −3 = 1