EVALUATING PIECEWISE FUNCTIONS WORKSHEET

Problem 1 :

Evaluate the following.

(a)  18    (b)  17     (c)  14     (d)  20

Solution

Problem 2 :

Evaluate for the given value.

(a)  -8    (b)  undefined     (c)  8     (d)  -4

Solution

Problem 3 :

Evaluate for the given value.

(a)  -2    (b)  17    (c)  4     (d)  -4

Solution

Problem 4 :

Evaluate for the given value.

(i)  f(-4)     (ii)  f(6)      (iii)  f(-2)      (iv)  f(0)

Solution

Problem 5 :

(i) f(8)      (ii)  f(0)       (iii)  f(4)       (iv)  f(5)

Solution

Problem 6 :

(i) f(0)      (ii)  f(5)       (iii)  f(2)       (iv)  f(-3)

Solution

Problem 7 :

(i) f(-5)      (ii)  f(11)       (iii)  f(0)       (iv)  f(3)

Solution

Problem 8 :

On a trip, the total distance (in miles) you travel in x hours is represented by the piecewise function

a. Interpret the domain and range of the function.

b. How far do you travel in 4 hours?

c. Compare the first 2 hours of the trip to the last 3 hours by calculating and interpreting the average rates of change

Solution

Problem 9 :

Describe and correct the error in graphing

Solution

Evaluate the following functions from the graph given below

Problem 1 :

(i)  𝑓(2) =       (ii)  𝑓(−3) =        (iii)  𝑓(−1) =       (v)  𝑓(−4) =

Solution

Problem 2 :

Evaluate 

(i)  𝑓(0) =    (ii)  𝑓(−4) =     (iii)  𝑓(−1) =      (iv)  𝑓(3) =

Solution

Problem 3 :

Evaluate the following :

a) 𝑓(−1) =     b) 𝑓(2) =   c) 𝑓(1) =   d) 𝑓(−2) =     e) f(0) = 

Solution

Problem 4 :

Evaluate the following :

𝑎. 𝑓(−3) =      b. 𝑓(4) =     c. 𝑓(1) =    d. 𝑓(−1) =    e. 𝑓(0) =

Solution

Problem 5 :

Evaluate the following :

𝑎. 𝑓(3) =   b. 𝑓(−1) =    c. 𝑓(−3) =     d. 𝑓(2) =     e. 𝑓(0.5) =

Solution

Problem 6 :

Evaluate the following :

𝑎. 𝑓(−4) =   b. 𝑓(1) =     c. 𝑓(3) =     d. 𝑓(2) =      e. 𝑓(1.5) =

Solution

Problem 7 :

If you earned upto $113700 in 2013 from an employer, your social tax rate was 6.2% of your income. If you earned over $113700, you pay a fixed amount of $7049.40

a) Write a linear piecewise function to represent the social security taxes for incomes between $0 and $500,000

b) How much scoial security tax would somone who made $50000 owe ?

c)  How much money would you have made if you paid $4000 social security tax in 2013.

d) What is the meaning of f(150000)? What is the value ?

Solution

Problem 8 :

During snow strom, a meterlogist tracks the amount of accumulating snow. For the first three hours of the strom, the snow fell at a constant rate of one inch per hour. The strom then stopped for two hours and then started again at a constant rate of one half inch per hour for next four hours.

a) create a graph of the situation

b)  When will the depth of the snow be 4 inches 

c)  How much snow will be there be on the ground after 4 hours.

d) Write the piecewise function that models the depth of the snow as the function of time.

Solution