COMPARING FUNCTIONS
Name of
Function
Describe the
graph using a
letter or words
Sketch
Does it have a
vertex?
Where does the
table start?
Linear
Quadratic
Exponential
Absolute Value
1. Complete the following tables and answer the questions to the right.
(a)
x
y = (½)x + 2
⧍y
This function is: linear  quadratic  exponential  absolute value
The function is:  positive
 negative
 growth
 decay
How can you verify the type of function selected? (name 2 ways)
(b)
x
y =(x + 4)2 - 2 ⧍y
This function is: linear  quadratic  exponential  absolute value
The function is:  positive
 negative
 growth
 decay
How can you verify the type of function selected? (name 2 ways)
(c)
x
y = -|x - 6| - 3
⧍y
This function is: linear  quadratic  exponential  absolute value
The function is:  positive
 negative
 growth
 decay
How can you verify the type of function selected? (name 2 ways)
(d)
x
y = -2x+5
⧍y
This function is: linear  quadratic  exponential  absolute value
The function is:  positive
 negative
 growth
 decay
How can you verify the type of function selected? (name 2 ways)
Use differences to identify the type of function represented by the table of values and tell whether they are
positive, negative, growth or decay. Write it in the space to the left of each table. Then below each table, name
two reasons why you named each function the way you did. (next to a and b)
2.
x
y
x
Y
x
y
x
y
-4
-5
-5
-2
-2
-.75
-3
11
-3
-3
-4
-3
-1
-.5
-2
5
-2
-1
-3
-4
0
0
-1
3
-1
1
-2
-3
1
1
0
5
0
3
-1
-2
2
3
1
11
a)
a)
a)
a)
b)
b)
b)
b)
3. Check all that apply.
a.
linear

b. y | x  5 | 7
linear
 quadratic 
quadratic
 exponential

exponential
 absolute value 
absolute value  positive  negative
positive
 negative  growth 
 growth  decay
decay
1
y 
 3
x
c. y   x  32  4
linear
 quadratic 
exponential
 absolute value 
positive
 negative  growth 
decay
e. y  3
linear
 quadratic
 exponential
 absolute value
 positive  negative  growth 
decay
x
d. y  2 x  5
linear
 quadratic 
exponential
 absolute value 
positive
 negative  growth 
decay
f. y  x  2  4 linear

quadratic
 exponential

absolute value  positive  negative
 growth  decay
2
g. Explain how to tell the difference between when a function is positive, negative, growth, or decay by looking at the
equation.
4. Graph the functions from the tables at very top of the page (part 2)
a) What type of function shows a constant rate of change in its y values?
b) Which functions change directions at the vertex?
c) Which function starts out increasing slowly and then ends by increasing rapidly?
d) Which type of functions increase or decrease the entire time?
e) Which type of functions increase and decrease over the course of the graph?
5. Create a table for each type of function:
Linear Positive
x
y
Linear Negative
x
y
Abs Value Positive
Abs Value Negative
x
y
x
y
6. Write an equation for each type of function:
Linear Positive
Linear Negative
Abs Value Positive
Abs Value Negative
7. Sketch a graph for each type of function:
Linear Positive
Linear Negative
Abs Value Positive
Abs Value Negative
Exponential Growth
x
y
Quadratic Positive
x
y
Exponential Growth
Quadratic Positive
Exponential Growth
Quadratic Positive
Exponential Decay
x
y
Quadratic Negative
x
y
Exponential Decay
Quadratic Negative
Exponential Decay
Quadratic Negative