Functions Practice Packet 1
Algebra 1
Name:
1) Describe in your own words each term below. Give examples for each.
a) What is a relation?
b) What is a function?
c) What is the domain of a relation/function and what is the range of a relation/function?
d) What makes a function an exponential function? Give an example of an exponential growth function
(equation and graph) and give an example of an exponential decay function (equation and graph).
e) What makes a function a linear function? (Give examples of equations and graphs.)
f) What makes a function an absolute value function? (Give examples of equations and graphs.)
g) What makes a function a quadratic function? (Give examples of equations and graphs.)
h) What makes a function a piecewise function? (Give examples of equations and graphs.)
2) Identify each scenario below as a linear, quadratic, exponential, absolute value, piecewise, or an other
type of function. Sketch a quick graph of each function and be sure to label the axes.
a) Karis earns $10/hr mowing lawns. The function that relates his total income, y, as a function of the
number of hours he works, x, is what type of function?
b) Lorenzo puts $1000 in the bank and the money earns 2% interest each year, compounded annually.
The function that relates the money in his account, M, as a function of the number of years the money
is in the bank, t, is what type of function?
c) Franny is walking on the first floor, then walks up the stairs at a constant rate, and then walks on the
second floor. If we look at her elevation in relation to time, the function would be what type of
function?
d) Caroline puts a chemical in a petri dish of about 5000 bacteria that causes the population of bacteria to
decline at a rate of 20% each minute. If b(x) is the number of bacteria at x minutes, what type of
function is b(x)?
e) Jamie walks slowly from one end of a balance beam to the other side of the balance beam. If we
measure Jamie’s distance, d, from the center of the balance beam at at every second, s, what type of
function would this be?
f) Each year, a ranger estimates the number of deer in a preserve over 5 years. See the table below,
where x is the time in years and g(x) is the number of deer (rounded to the nearest hundred).
x
g(x)
0
120
1
130
2
140
3
150
4
160
5
170
g) Another ranger keeps track of the number of deer in her preserve over 4 years.
where x is the time in years and f(x) is the number of deer.
x
f(x)
0
80
1
120
2
180
3
270
4
405
See the table below,
3) Write an equation for the functions described above in #2a, 2b, 2d, 2f, and 2g
4) Given each function below, answer the questions below.
f ( x)  3 x  2
1
j ( x)  100 
2
G ( x)  x  1
m( x)  x  2  5
2
x
 2, x  0

N ( x)   x  2, 0  x  3
4, x  3

a) Identify each type of function.
b) State the domain and range of f (x) .
c) State the domain and range of G (x) .
d) State the domain and range of m(x) .
e) Challenge: State the domain and range of N (x) .
f) Evaluate f (7) .
g) Evaluate j (3) .
h) Evaluate m(6) .
i) Evaluate N (2.5) .
j) Put in order from smallest to biggest: G (2) , G ( 1 ) , f (2) , and m(20)
2
5) Solve each equation below graphically. To show your work: show what you entered for y1 and y2 ;
make a sketch of the graph and/or table that you used; indicate the window you used; clearly state the
solution(s).
b)  2 x  1  5  (2)
a) x  x  3x  5
2
x
6) Sydney was studying the following functions:
𝑓(𝑥) = 2𝑥 + 4 and 𝑔(𝑥) = 2(2)𝑥 + 4
She said that linear functions and exponential functions are basically the same. She made her
statement based on plotting points at 𝑥 = 0 and 𝑥 = 1 and graphing the functions.
Help Sydney understand the difference between linear functions and exponential functions by
comparing and constrasting 𝑓 and 𝑔. Support your answer with a written explanation that includes
use of the average rate of change and supporting tables and/or graphs of these functions.