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 = x 2 – 9x – 12 using a table of values Graph the function y = x 2 – 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: 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 = r 2 ; (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 = r 2 ; (h, k) is the center of the circle r = radius of the circle Example: Graph a circle with the equation x 2 + (y + 6) 2 = 25

Group Work Problems 1.Is a solution to the equation 18x – 12y = 18? 2.Use intercepts (x & y) to graph -3x + 8y = Graph the equation y = x 2 – 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. Helen Mirren Jennifer Hudson Leonardo DiCaprio Jamie Foxx The Queen Blood Diamond Dreamgirls The Departed 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) = 2x 2  x + 3. Find each of the following. a. f (0) f (0) = 2(0) 2  = 0 – = 3 b. f (–7) f (–7) = 2(–7) 2  (–7) + 3 = = 108

1.2 Topic: Finding the value of a function A function is given by f(x) =.. Find each of the following. a. f (2) = b. f (–6) = c. f(-3/4)

1.2 Topic: Finding the value of a function A function is given by f(x) =.. Find each of the following. a. f (5) = b. f(-1/3)

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. 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. 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 and 2.Find the midpoint of and 3.f(x) = ; Find a) f(-12) and b) f( ) 4.Estimate the domain and range of the following functions: