1. I. Evaluating Piecewise Functions
Pre-Calc/ Trigonometry Name: _________________________
Piecewise Functions Notes Date: __________________________
Piecewise Functions –
A combination of equations, each corresponding to a part of the domain (x-values).
Example:
f x = 2x−1, x≤1 3x+1, x>1
I. Evaluating Piecewise Functions
f x = 2x−1, x≤1 3x+1, x>1
f x = x 2 −1, x<−1 x , −1≤x<1 2, x≥1
f(-2) b) f(0)
c) f(1) d) f(3)
f(-2) b) f(-1)
c) f(0) d) f(1)
II. Graphing Piecewise Functions
Example 2:
Example 1:
Example 3:
Example 4: Write the equation of the given piecewise function.
Erin buys gas at a self service stations for $2.75 a gallon. The gas station has a promotion going on that anyone who buys more than 10 gallons of gas, only has to pay $2.50 per gallon.
a. Write the piecewise function for total cost, C(g) as a function of g gallons of gas.
b. Determine how much it will cost to fill Erin’s tank of gas if it holds 12 gallons of gas.

2. 1) 2) 3) 4) Evaluate: Evaluate: f(-1)= ____ f(-1)= ____ f(0)= ____
Pre-Calculus/Trig Name __________________________
Piecewise Functions Classwork Date _______________ Block ______
Directions: Graph each piecewise function., then evaluate at the given values. 1) 2)
Evaluate:
f(-1)= ____
f(0)= ____
f(3)= ____
Evaluate:
f(-1)= ____
f(0)= ____
f(2)= ____ 3) 4)
f(x)= x−1 − x<1 x x≥1
Evaluate:
f(-1)= ____
f(0)= ____
f(3)= ____
Evaluate:
f(-1)= ____
f(1)= ____
f(3)= ____
5) The amount of Social Security tax you pay, depends on your annual income. As of 2015 you pay 6.2 % of your income if it is less than $118,500. If your income is at least $118,500, you pay a fixed amount of $7,347.
a.) Write the piecewise function.
b.) If Ms. Howard made $33,000 last year how much did she pay in social security?
6) Write the equation of the given piecewise function.

3. Pre-Calculus/Trig Name __________________________
Piecewise Functions Homework Date _______________ Block ______ 1. 2.
Evaluate:
f(-4)= ____
f(0)= ____
f(3)= ____
Evaluate:
f(-1)= ____
f(0)= ____
f(3)= ____ 3. 4.
Evaluate:
f(-1)= ____
f(0)= ____
f(3)= ____
Evaluate:
f(-1)= ____ f(-3)= ____
f(3)= ____ f(0)= ____

4. Pre-Calculus/Trig Name __________________________
Piecewise Functions Homework Date _______________ Block ______
5. The amount d (in billions of dollars) spent on prescription drugs in the United States from 1991 to 2002 can be approximated by the model
𝑑 𝑡 = 5𝑡+37, 1≤𝑡≤7 18.7𝑡−62, 8≤𝑡≤12
Use this model to find the amount spent on prescription drugs in each year from 1991 to 2002.
6. Write the equation of the given piecewise function.
7. Write the equation of the given piecewise function.