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Grade 10

Grade 10. TAKS Preparation Unit Objective 1. 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

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Grade 10

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  1. Grade 10 TAKS Preparation Unit Objective 1

  2. 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. Independent and Dependent Quantities, continued… • In an equation, x represents the independent quantity and y represents the dependent quantity Ex: y = 2x + 3 Dependent Independent 1, A.01A

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

  5. 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

  6. 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, A.01B

  7. 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? • y = 2x² - 4 • y = 3x² - 4 • y = 2x² + 4 • y = 3x² + 4 1, A.01B

  8. Writing and Interpreting Equations • These problems are always LINEARequations 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

  9. 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 Slope is how much the value increases = 545 Y intercept is the beginning (initial) value of the stock = 2000 1, A.01C

  10. -2 0 1 2 -7 -1 2 5 Multiple Representations of Functions y = 3x - 1 • A function can be represented by an: • Equation • Mapping • Graph • Table • Data Points • Verbal Description f(x) = {(-2, -7), (0, -1), (1, 2), (2, 5)} y is a number one less than three times x 1, A.01D

  11. x y 1 2 3 4 3 6 9 12 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)? A. 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} B. Since the x’s and y’s have been switched, B is not a correct representation. 1, A.01D

  12. Creating a Table • To create a table from a situation • Write an equation • Put your equation in y= • Find a table that matches 1, A.01D

  13. 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 B b = 50 – 6.75m 1. Write an equation 2. Put equation in y= C D 1, A.01D

  14. 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 < or > A solid line ≤ or  Shaded above  or > Shaded below ≤ or < 1, A.01D

  15. Graphs of Inequalities, continued… • y < -2x +1.5 • y < -2x + 3 • y ≤ -2x + 3 • y < 2x + 3 Example: Y intercepts are not the same Not the same line! 1, A.01D

  16. 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, A.01E

  17. 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, A.01E

  18. No movement 1000 ft in 1 min fastest speed 1000 ft in 2 min or 500 ft per min 500 ft in 2 min or 250 ft per min 500 ft in 1 min Interpreting Graphs, cont… • The slope of lines indicates speed • Steep line means rapid speed • Flat line means no movement 2, A.01E

  19. -1 0 1 2 2 5 8 11 Essential Vocabulary y = 3x + 5 • Independent • Dependent • Variable • Equation • Table • Inequality • Mapping • Graph y = 3x + 5 y = 3x + 5 y = 3x + 5 y < 3x + 5

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