© A Very Good Teacher 2007 Algebra 1 EOC Preparation Unit Objective 2 Student Copy Independent and Dependent Quantities Independent and Dependent Quantities must be variables (letters), not constants (numbers). Independent Quantities are often quantities that cannot be controlled Dependent Quantities change as a result of the Independent Quantities 1, Ab1A Algebra 1 EOC Preparation Unit Objective 2:

© A Very Good Teacher 2007 Parent Functions There are two parent functions on the TAKS test: 2, Ab2A y = x y = x²

© A Very Good Teacher 2007 Domain and Range ______ is the set of all x values ______ is the set of all y values To find domain: examine the ___________ boundaries of the function To find range: examine the ____________ boundaries of the function Whenever a function has two boundaries, both signs should be less than (< or ≤). 2, Ab2B

© A Very Good Teacher 2007 Domain and Range, cont… Example of finding the Domain Domain: ____ < x ≤ ____ 2, Ab2B

© A Very Good Teacher 2007 Domain and Range, cont… Example of finding the Range Range ____ ≤ y < ____ 2, Ab2B

© A Very Good Teacher 2007 Interpreting Graphs Pay attention to labels on x and y axes A straight line indicates ________ rate of change (slope) A curved line indicates a _______ rate More than one straight lines indicates ______ _______ constant rates 2, Ab2C

© A Very Good Teacher 2007 Interpreting Graphs, cont… The _____ of lines indicates speed –Steep line means rapid speed –Flat line means no movement 2, Ab2C

© A Very Good Teacher 2007 Scatter Plots Correlation 2, Ab2D

© A Very Good Teacher 2007 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 … Per, each, dividend … Mean … Is or other verbs … Mean … The goal is to turn a sentence into an equation. 3, Ac3A

© A Very Good Teacher 2007 Using symbols, cont… Here is a simple example: The area of a circle is equivalent to pi times the radius squared. 3, Ac3A

© A Very Good Teacher 2007 Patterns Given a geometric sequence, you must determine the equation for the function. 1.Make a table to represent the sequence 2.Use STAT to calculate the answer 3.Find the answer that fits the calculator answer 3, Ac3B

© A Very Good Teacher 2007 Patterns, cont… Here’s an example: Figure# of squares Make a table 3, Ac3B

© A Very Good Teacher 2007 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 (x in L1 & y in L2)

© A Very Good Teacher 2007 Solving Equations and Inequalities __________ 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? 3, Ab4A

© A Very Good Teacher 2007 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 __ the inequality sign! Example: 4x – 2y ≤ 5 3, Ab4A

© A Very Good Teacher 2007 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 ___ values and dependent variables represent ___ values Just use the calculator to graph the function and look at the table to identify the corresponding y values 3, Ab4A

© A Very Good Teacher 2007 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? 3, Ab4A

© A Very Good Teacher 2007 Simplifying Expressions Use properties to simplify completely Example: Which expression is equivalent to (5t – 4)6t – (5t – 4)(t + 1)? 3, Ab4B