Section 1.1 & 1.2
Most people burn more calories while sleeping than while
watching ______________________________________
TV… so turn off your laptop/tv/ipad and sleep!
1.1 Topic: The coordinate plane.
What is the coordinate plane?
Identify the following points on the coordinate plane…
If x represents the unemployment rate
and y represents the median weekly
earnings, write as a coordinate for
Master’s Degree, Associated Degree,
and High School Diploma
1.1 Topic: Checking whether a point is a solution
What is a solution to an equation?
Check whether (5, -7) is a solution to 2x – 3y = 30
Check whether (10/3, 8/5) is a solution to 6x + 15y = 44
1.1 Topic: x-intercept and y-intercept
What do you know about an x-intercept and y-intercept?
Given the equation: 7x – 2y = -14……………..
a) How do you find the x-intercept?
b) How do you find the y-intercept?
c) Graph the equation using x-int and y-int
1.1 Topic: Graphing lines using slope-intercept form
What is slope-intercept form?
a) Write 3x – 5y = 20 in slope-intercept form
b) Write –6x + 7y + 21 = 0 in slope-intercept form
Graph both lines in ‘a’ and ‘b’ using slope-intercept form
1.1 Topic: Graphing quadratic functions using a table of values
Graph the function y = x2 – 9x – 12 using a table of values
Graph the function y = x2 – 9x – 12 using a graphing calculator
1.1 Topic: The distance formula
Suppose that Santa Ana College is ground zero. Now, suppose that
you travel 4 miles south on Bristol, and 6 miles east on Warner Ave.
How far are you diagonally from SAC?
Hint: Remember the Pythagorean theorem.
Using this concept, find the distance between the following points:
(-3, -2) and (5, -8)
1.1 Topic: The distance formula
You can also use the distance formula to find the length of a side:
1.1 Topic: The distance formula
Plot the following points on a coordinate plane:
(6, 1) (0, 4) (-6, -8)
Connect the points to make a triangle
Find the length of each side using the distance formula
Is this a right triangle?
1.1 Topic: The midpoint formula
The midpoint formula:
 x1  x2 y1  y2 
,


2 
 2
Find the midpoint of the segment: (-3, -6) and (7, 2)
Graph to verify
1.1 Topic: The equation of a circle
The equation of a circle is given by the formula:
(x – h)2 + (y – k)2 = r2 ;
(h, k) is the center of the circle
r = radius of the circle
Example: Find the equation of a circle with center at (-3, 5) and
radius = 6cm.
1.1 Topic: The equation of a circle
The equation of a circle is given by the formula:
(x – h)2 + (y – k)2 = r2 ;
(h, k) is the center of the circle
r = radius of the circle
Example: Graph a circle with the equation x2 + (y + 6)2 = 25
Group Work Problems
1. Is
5 1
 , 
6 4
a solution to the equation 18x – 12y = 18?
2. Use intercepts (x & y) to graph -3x + 8y = -24
3. Graph the equation y = x2 – 2x + 3 by plotting 5 points
4. Plot the following points: (-5, 6) (2, 0), (3, 4), find the distance, and
verify whether the triangle is a right triangle.
5. Find the equation of a circle with the center (-5, 2) and r = 3cm
1.2 Topic: Domain, Range, and Function
A function is a relation in which each value in the domain is paired up
with only ONE value in the range.
Determine if the following correspondences are functions.
Ex: Significant others….
Ex:
Ex:
• Determine whether each of the following correspondences
is a function.
The Queen
Helen Mirren
Blood Diamond
Jennifer Hudson
Dreamgirls
Leonardo DiCaprio
The Departed
Jamie Foxx
This correspondence is not a function because there
is one member of the domain (Leonardo DiCaprio)
that is paired with more than one member of the
range (Blood Diamond and The Departed).
1.2 Topic: Domain, Range, and Function
Domain: all values of x
Range: all values of y
Identify the domain and range. Determine whether each of the following
relations is a function.
{(–2, 5), (5, 7), (0, 1), (4, –2)}
Domain is the set of first coordinates: {–2, 5, 0, 4}.
Range is the set of second coordinates: {5, 7, 1, –2}.
Is the relation a function?
Do the graphs above represent functions
 (does each x have one y value?)
You can use the VERTICAL LINE TEST to determine if a
graph is a function
1.2 Topic: Finding the value of a function
A function is given by f(x) = 2x2  x + 3. Find each of the following.
a. f (0)
f (0) = 2(0)2  0 + 3 = 0 – 0 + 3 = 3
b. f (–7)
f (–7) = 2(–7)2  (–7) + 3 = 2 • 49 + 7 + 3 = 108
1.2 Topic: Finding the value of a function
x4
A function is given by f(x) = .
. Find each of the following.
x6
a. f (2) =
b.
f (–6) =
c.
f(-3/4)
1.2 Topic: Finding the value of a function
2
A function is given by f(x) = .
6 x
a. f (5) =
b.
f(-1/3)
. Find each of the following.
2
1.2 Topic: Finding the value of a function using a graph
f(-2) =
f(1) =
f(??) = 2
1.2 Topic: Finding Domain and Range using a graph
Graph the function. Then estimate the domain and range.
f ( x) 
x4
D: All possible values of X
R: All possible values of Y
1.2: Finding Domain and Range using a graph
Graph the function. Then estimate the domain and range.
f ( x) 
x4
D: All possible values of X
R: All possible values of Y
1.2: Finding Domain and Range using a graph
Estimate the domain and range.
D: All possible values of X
R: All possible values of Y
1.2: Finding Domain and Range using a graph
Estimate the domain and range.
D: All possible values of X
R: All possible values of Y
1.2: Finding Domain and Range using a graph
Estimate the domain and range.
D: All possible values of X
R: All possible values of Y
Group Work Problems
1. Find the distance between  5 , 1  and  4 , 1 
6
4
3
4
2. Find the midpoint of  56 , 41  and  34 , 34 
3. f(x) =
x7
;
2x  4
Find a) f(-12) and
2
b) f( 3)
4. Estimate the domain and range of the following functions: