1. © A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 1

2. © A Very Good Teacher 2007 Independent and Dependent Quantities Independent and Dependent Quantities must be variables (letters), not constants (numbers). Independent Quantities are often quantities that cannot be controlled –Ex: time and weather Dependent Quantities change as a result of the Independent Quantities –Ex: distance and number of ice cream cones sold 1, A.01A

3. © A Very Good Teacher 2007 Independent and Dependent Quantities, continued… In an equation, x represents the independent quantity and y represents the dependent quantity Ex: y = 2x + 3 1, A.01A DependentIndependent

4. © A Very Good Teacher 2007 Independent and Dependent Quantities, continued… Sometimes equations have other variables, not x and y. Ex. d = 54t DependentIndependent The variable by itself is always dependent! 1, A.01A

5. © A Very Good Teacher 2007 Independent and Dependent Quantities, continued… When no equation is given: 1, A.01A A car salesman made a chart showing the relationship between the number of cars he sells and the months of the year. Now ask yourself, does the number of cars depend on the months of the year or do the months of the year depend on the number of cars? Because the number of cars will change based on the month, the number of cars is dependent, and the month is independent.

6. © A Very Good Teacher 2007 Functions and their equations A function is relationship where each x is paired with only one y. In other words, the x’s cannot repeat! 1, A.01B xy 02 13 24 36 FunctionNot a Function xy 02 13 14 36

7. © A Very Good Teacher 2007 Functions and their equations, continued… To identify a function in a graph you must use a vertical line test. 1, A.01B Since the vertical red line only touches the function (in green) at one point at a time, this is a function.

8. © A Very Good Teacher 2007 Functions and their equations, continued… Is this a function? 1, A.01B Since the vertical red line touches the relation (in green) at 2 points at a time, this is not a function.

9. © A Very Good Teacher 2007 Functions and their equations, continued… To find the equation of a function when you are given the table, use the feature of your graphing calculator. Enter the table into the calculator using L1 for x and L2 for y. Then return to and arrow over to CALC and choose the appropriate function type. Press Enter to view equation. 1, A.01B

10. © A Very Good Teacher 2007 Functions and their equations, continued… How do I know what type of function to use? All TAKS questions will either be Linear (LinReg, ax+b) or Quadratic (QuadReg) If you aren’t sure look at the answers and see if they are linear or quadratic. 1, A.01B

11. © A Very Good Teacher 2007 Functions and their equations, continued… Here’s one to try: The table below shows the relationship between x and y. Which function best represents the relationship between the quantities in the table? xy 0-4 1 28 1, A.01B A. y = 2x² - 4 B. y = 3x² - 4 C. y = 2x² + 4 D. y = 3x² + 4

12. © A Very Good Teacher 2007 Writing and Interpreting Equations These problems are always LINEAR equations or inequalities. You will need to identify the slope (amount of change) and the y intercept (starting point) Pay careful attention to math cue words each means multiply increased means add decreased means subtract difference means subtract 1, A.01C

13. © A Very Good Teacher 2007 Writing and Interpreting Equations, continued… Example: The initial amount invested in a stock was $2000. Each year the stock increases in value by $545. Which equation represents t, the total value of the investment after y years? A. t = 2000y + 545 B. t = 2000y – 545 C. t = 545y + 2000 D. t = 545y - 2000 1, A.01C Slope is how much the value increases = 545 Y intercept is the beginning (initial) value of the stock = 2000

14. © A Very Good Teacher 2007 Graphs of Functions You will be asked to match an equation or table to a graph. Your graphing calculator can assist you in these problems. 1, Ab1D

15. © A Very Good Teacher 2007 Graphs of Functions, continued… When you are given a graph and asked to find the equation… Use your calculator to graph all the answers and find one that matches! 1, Ab1D A. y =.5x² + 3 B. y =.5x² – 3 C. y = 2x² + 3 D. y = 2x² - 3

16. © A Very Good Teacher 2007 Graphs of Functions, continued… When you are given a table and asked to find the graph that matches it… Graph all the points and see which graph contains all of them 1, Ab1D xy 1 00 11 24 AB C D

17. © A Very Good Teacher 2007 Graphs of Functions, continued… When given the graph of a linear inequality and asked to find the equation… Use your calculator to graph each inequality (ignoring the inequality sign) Then narrow down your choices and pay attention to details A dotted line A solid line ≤ or  Shaded above  or > Shaded below ≤ or < 1, Ab1D

18. © A Very Good Teacher 2007 Graphs of Functions, continued… Let’s try one: 1, Ab1D A. y < -2x +1.5 B. y < -2x + 3 C. y ≤ -2x + 3 D. y < 2x + 3

19. © A Very Good Teacher 2007 Interpreting Graphs, Charts and Equations When you are given a graph and asked make a conclusion… Pay attention to the details! What does the x axis represent? Years? Time? What does the y axis represent? Dollars? Thousands of dollars? Watch for increased units. 1, A.01E

20. © A Very Good Teacher 2007 Interpreting Graphs, Charts and Equations, continued… When asked to make a prediction from a graph or chart… Make a table or extend the existing table Watch for gaps in the chart! 1, A.01E Year# of roads 197815 198225 198635 199250 +4 +6 +10 +15 How many roads will there be in 2002? 1998 200275 65 +15 +10 +6 +4

21. © A Very Good Teacher 2007 Interpreting Graphs, Charts and Equations, continued… When interpreting equations remember that they are LINEAR situations Identify the slope (rate of change) and the y intercept (beginning value) Pay close attention to the details like decimals that represent percents 1, A.01E

22. © A Very Good Teacher 2007 Interpreting Graphs, Charts and Equations, continued… Let’s try one… 1, A.01E Carla uses the function f(x) = 125 +.15x, where x is her weekly sales, to calculate her weekly salary. The best interpretation of this situation is that Carla will earn… A.$125 plus 15% of the store’s total weekly sales B.$125 plus 15% of her weekly sales C.$125 plus 15% of the store’s weekly profit D.The same amount regardless of her sales Slope or rate of change… here it is a decimal that represents a percent. Y intercept or beginning value