Section 4-7 Day 2
Graphing Functions
Objective: Students will use function notation
to graph and compare parent graphs.
Standard: A.CED.2 , F.IF.7 , F.BF.3, F.IF.2
Example 1
Find the value of x so that the function has the
given value.
f(x) = 3x – 2 ; 10
This means f(x) = 10. Solve for x.
f(x) = 3x – 2
10 = 3x – 2
+2
+2
12 = 3x
3
3
4=x
Parent Functions and Families of Functions
• A family of functions is a group of functions with
similar characteristics.
• For example: functions of the form f(x) = mx + b
constitute the family of linear functions.
• The most basic linear function in the family is
called the parent linear function, which is:
f(x) = x
Y-intercept = b = 0
Slope = m = 1
(-1,-1)
(-2,-2)
(2,2)
(1,1)
(0,0)
Example 2
• Changing the y-intercept will SHIFT your
parent function up or down.
Graph f(x) = x and the following on the same graph.
Compare the graph with the graph of f(x) = x
f(x) = x
a. f(x) = x + 4
Shifts UP 4
b. f(x) = x – 3
Shifts DOWN 3
In General:
If b > 0, Shift UP
If b < 0, Shift DOWN
Example 3
• Changing the SLOPE will change the
STEEPNESS of your parent function. Also
called stretch or shrink.
Graph f(x) = x and the following on the same graph.
Compare the graph with the graph of f(x) = x
f(x) = x
a. f(x) = 3x
Steeper or Stretch
b. f(x) = ½ x
Less steep or Shrink
c. f(x) = -2x
Reflects and
Steeper/Stretch
In General for Slope:
•
If |m| > 0, then the graph is STEEPER
or a STRETCH.
•
If 0< |m| < 1 (basically a fraction less than
one), then the graph is LESS STEEP or a
SHRINK.
•
If m is NEGATIVE , then the graph
REFLECTS.
Homework
Section 4-7
Pg. 266-267
14 - 17,
23 - 34, 39, 41, 42