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Exit Level

Exit Level. TAKS Preparation Unit Objective 2. Parent Functions. There are two parent functions on the TAKS test:. Linear. Quadratic. y = x ². y = x. Opens up. Vertex at (0, 0). y axis is axis of symmetry. 2, Ab2A. Domain and Range. Domain is the set of all x values

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Exit Level

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  1. Exit Level TAKS Preparation Unit Objective 2

  2. Parent Functions • There are two parent functions on the TAKS test: Linear Quadratic y = x² y = x Opens up Vertex at (0, 0) y axis is axis of symmetry 2, Ab2A

  3. Domain and Range • Domain is the set of all x values • Range is the set of all y values • To find domain: examine the right and left boundaries of the function • To find range: examine the top and bottom boundaries of the function • Whenever a function has two boundaries, both signs should be less than (< or ≤). 2, Ab2B

  4. Domain and Range, cont… • Example of finding the Domain Domain: ____ < x≤ ____ -3 2 2, Ab2B

  5. Domain and Range, cont… • Example of finding the Range Range ____ ≤ y < ____ 5 -4 2, Ab2B

  6. 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, Ab2C

  7. 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, Ab2C

  8. Scatter Plots Correlation PositiveNegativeNo 2, Ab2D

  9. Using symbols • Focus on the meaning of words in a mathematical context • For Example: More, more than, in addition, …. Mean … + Less, less than, difference …. Mean … - Times, per, each, … Mean … x Per, each, dividend … Mean … ÷ Is or other verbs … Mean … = The goal is to turn a sentence into an equation. 3, Ac3A

  10. Using symbols, cont… Here is a simple example: The area of a circle is equivalent to pi times the radius squared. A = π • r ² So, you would look for the answer A = πr² 3, Ac3A

  11. Patterns • Given a geometric sequence, you must determine the equation for the function. • Make a table to represent the sequence • Use STAT to calculate the answer • Find the answer that fits the calculator answer 3, Ac3B

  12. Patterns, cont… Make a table • Here’s an example: 3, Ac3B

  13. Patterns, cont… • Now use STAT to calculate the equation. STAT ENTER NUMBERS STAT  5, ENTER Look for an answer that has an equation like y = x². 3, Ac3B

  14. Solving Equations and Inequalities • Substitute given values • Use inverse operations to solve • Example:If (2.25, y) is a solution to the equation 4x – 2y = 8, what is the value of y? 4x – 2y = 8 4(2.25) – 2y = 8 y = ½ 9 – 2y = 8 -9 -9 – 2y = -1 -2 -2 3, Ab4A

  15. Solving Equations and Inequalities, cont… • Convert inequalities from Standard form (Ax + By > C) to y = mx + b form. • Use the same steps as you would for an equation, but remember that if you multiply or divide by a negative number, you must flip the inequality sign! • Example: 4x – 2y ≤ 5 - 4x - 4x -2y ≤ -4x + 5 Because you divided by a negative, you must flip the ≤ to ! -2 -2 -2 y  2x – 2.5 3, Ab4A

  16. Solving Equations and Inequalities, cont… • Given a function like y = 3x² + 2x – 4 and a set of independent variables like {-1, 0, 1, 2} and asked to find a corresponding dependent variable • Remember that independent variables represent the x values and dependent variables represent y values • Just use the calculator to graph the function and look at the table to identify the corresponding y values 3, Ab4A

  17. Solving Equations and Inequalities, cont… • Example:A function is described by the equation y = 3x² + 2x – 4, in which y is dependent on x. If a value for the independent variable is selected from the set {-1, 0, 1, 2}, which of the following is a corresponding dependent value? The answer must be from the y values that correspond to the x values listed in the question. So, the answer must be one of {-3, -4, 1, 12}. 3, Ab4A

  18. Simplifying Expressions • Use properties to simplify completely • Example: Which expression is equivalent to (5t – 4)6t – (5t – 4)(t + 1)? Multiply to eliminate parentheses 30t² - 24t - ( 5t² +5t - 4t - 4) 30t² - 24t – 5t² - 5t + 4t + 4 Combine like terms 25t² -25t + 4 3, Ab4B

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