2.1 Functions and Their Graphs and 2.2 Slope and Rate of Change
6
RECALL:
coordinate plane – cartesian plane or x-y plane
ordered pairs – points in the form (x, y)
x-coordinate – first value in an ordered pair.
y-coordinate – the second value in an ordered pair.
4
2
-5
5
-2
-4
-6
1.) Can you identify a difference between the graphs that are functions and the graphs that are NOT function?
Method 1:
Method 2:
2.) Using either method 1 or method 2 decide which of the following graphs are functions?
function – a set of ordered pairs for which there is exactly one y-value for each x-value.
For the following sets of ordered pairs answer questions below:
a.) Do the ordered pairs graph a function?(Method 1?)
b.) Using method 2, explain why the set of ordered pairs is or is not a function?
c.) What is the domain and range?
Example 1
Example 2
6
(−3,3)
(1,1)
(3,1)
(4, −2)
6
(−3,3)
(1, −2)
4
2
-5
(4,1)
(1, 4)
5
-2
4
2
-5
5
-2
-4
-4
-6
-6
Evaluating Functions
f ( x) = 3x 2 − 2 x + 7
f (−2)
Slope: a numerical value that represents the steepness of a line (m)
g ( x) = 4 x + 1
Slope = m =
g(7)
vertical change
rise
=
horizontal change run
Slopes of Graphs
s ( y)
2
-2
2
-2
= 2
2
2
-2
-2
Recall : The slope of a nonvertical line passing through the points ( x1 , y1 ) and ( x 2 , y 2 ) is m =
y 2 − y1
x 2 − x1
Find the slope of the line passing through the points and tell whether it rises, falls, is horizontal,
or vertical.
⎛1
⎞ ⎛3
⎞
a.) (4, 2) (-18, 1)
b.) (-7, 3) (-2, 3)
c.) ⎜ , −1⎟ ⎜ , −2 ⎟
⎝5
⎠ ⎝5
⎠
Find the slope of the below lines by graphing and then by using the slope formula. Decide which
slope is steeper and explain your answer.
Line 1: through (−1,−3) and (−3,−2)
Line 2: through (3,−4) and (0,−3)
SAT Type Problems:
Find the value of k so that the line through the given points has the given slope.
1.) (5,k) and (k,7), m=1
2.) ( -2, k) and (k,4), m=3
Word Problems:
A water park slide drops 8 feet over a horizontal distance of 24 feet. Find its slope. Is it going to be
positive or negative? Then find the drop over a 54 foot section with the same slope.
The slope of a road, or grade, is usually expressed as a percent. For example, if a road has a grade of
3%, it rises 3 feet for every 100 feet of horizontal distance.
a. Find the grade of a road that rises 75 feet over a horizontal distance of 2000 feet.
b. Find the horizontal length of a road with a grade of 4% if the road rises 50 feet over its
length.