Functions and Graphs Objective: Students will be able to identify different types of graphs and evaluate different properties about the graphs

Modeling and Interpreting Tables Be able to read and interpret a table Pg 81 HW What did you look for to help determine table and graph relationship? Pattern in the table linear, quadratic, possible x or y intercept Table and equation relationship? Pattern if linear was the slope y intercept or vertex

Designing an Algebraic Model Exploration 1 pg 72 A department store is having a sale in which everything is discounted 25% off the marked price. The discount is taken at the sales counter, and then a state sales tax of 6.5% and a local sales tax of 0.5% are added on.

The discount price d is related to the marked price m by the formula d=km, where k is a certain constant. What is k? .75 The actual sale price s is related to the discount price d by the formula s = d +dt, where t is a constant related to the total sales tax. What is t? 7% or .07 Using the answers from steps 1 and 2 you can find a constant p that relates s directly to m by the formula s = pm. What is p? 0.8025

If you only have $30, can you afford to buy a shirt marked $36.99? yes If you have a credit card but are determined to spend no more than $100, what is the maximum total of your marked purchases before you present them at the sales counter? $124.61

Fitting a curve to the data Using your calculator Make the table Stat, edit x axis is L1, y axis is L2 Plot points – set the window to stat plot Graph of best fit Stat Calc select type of graph you think it is, Stat L1,L2,Y1 The Y1 will put it into your graph so it will be graphed with the points

Interpreting the model Exploration 2 Percentage must be less than or equal to 100 2009 is still close to the data we are modeling

Zero Factor Property Solving an equation Graphically, Numerically or Algebraically Multiple methods Use what is most comfortable to you A product of real numbers is zero if and only if at least one of the factors in the product is zero

Fundamental Connection If a is a real number that solves the equation f(x)=0, then these three statements are equivalent. The number a is a root or solution of the equation f(x)=0 The number a is a zero of y=f(x) The number a is an x-intercept of the graph of y=f(x)

Rule of 4 Understand the problem What information is needed to solve the problem, what are they asking you to do Devise a plan Draw a picture if necessary, use and define variables Carry out the plan Solve and support the solution Look back Does the result make sense, label answer

Example The engineers at an auto manufacturer pay students $0.08 per mile plus $25 per day to road test their new vehicles. How much did the auto manufacturer pay Sally to drive 440 miles in one day? P=25+0.08x $60.20 John earned $93 test driving a new car in one day. How far did he drive? 850 miles

Objective: Students will be able to identify different types of graphs and evaluate different properties about the graphs On a scale of 1 to 4 Do you feel we meet the objective for the day. If we did not meet the objective, what did we miss and how could I improve.

HW Pg 81 1-10, 24 and 48