TAKS Preparation Unit Objective 1 Grade 9 Student Version TAKS Preparation Unit Objective 1

Independent and Dependent Quantities Independent and Dependent Quantities must be variables (_______), not constants (_________). Independent Quantities are often quantities that cannot be controlled Dependent Quantities change as a result of the Independent Quantities 1, Ab1A

Independent and Dependent Quantities, continued… In an equation, x represents the __________ quantity and y represents the _________ quantity Ex: y = 2x + 3 1, Ab1A

Independent and Dependent Quantities, continued… Sometimes equations have other variables, not x and y. Ex. d = 54t The variable by itself is always _________! 1, Ab1A

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, Ab1B

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 (y = x) or quadratic (y = x²). 1, Ab1B

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? x y -1 -4 1 2 8 y = 2x² - 4 y = 3x² - 4 y = 2x² + 4 y = 3x² + 4 B. y = 3x² - 4 1, Ab1B

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 ______ increased means _____ decreased means _______ difference means _______ 1, Ab1C

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? t = 2000y + 545 t = 2000y – 545 t = 545y + 2000 t = 545y - 2000 C. t = 545y + 2000 1, Ab1C

Multiple Representations of Functions A function can be represented by an: Equation Mapping Graph Table Data Points Verbal Description 1, Ab1D

Multiple Representations of Functions, cont… Example: The function f(x) = {(1, 3), (2, 6), (3, 9), (4, 12)} can be represented several ways. Which is NOT a correct representation of the function f(x)? 1 2 3 4 6 9 12 x y A. B. C. x is a natural number less than 5 and y is 3 times x D. y = 3x and the domain is {1, 2, 3, 4} A. y = .5x² + 3 1, Ab1D

Creating a Table To create a table from a situation Write an equation Put your equation in y= Find a table that matches A. Quadratic parent function 1, Ab1D

Creating a Table, cont… Example: Carmen receives a $50 gift card to the local movie theater. Each movie she watches costs $6.75. Which table best describes b, the balance on her gift card after she watches m movies? A m b 1 6.75 5 33.75 7 47.25 B m b 50 1 56.75 5 83.75 7 97.25 m b 1 43.25 2 36.50 4 29.75 7 23 m b 50 1 43.25 5 16.25 7 2.75 C D 1, Ab1D

Graphs of Inequalities 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 Shaded above Shaded below 1, Ab1D

Graphs of Inequalities, continued… Example: y < -2x +1.5 y < -2x + 3 y ≤ -2x + 3 y < 2x + 3 B. y < -2x + 3 1, Ab1D

Interpreting Equations When you are given a function and asked make a conclusion… Use your calculator! Example: Which is always correct about the quantities in the function y = x – 3? The variable y is always 3 more than x The variable x is always greater than the variable y When the value of x is negative, the value of y is positive As the value of x increases, the value of y decreases 1, Ab1E

Interpreting Graphs Pay attention to labels on x and y axes A straight line indicates constant rate of change (slope) A curved line indicates a changing rate More than one straight lines indicates rapidly changing constant rates 2, Ab1E

Interpreting Graphs, cont… The slope of lines indicates speed Steep line means rapid speed Flat line means no movement 2, Ab1E

Essential Vocabulary Independent Dependent Variable Equation Table Inequality Mapping Graph