© A Very Good Teacher 2007 Grade 10 TAKS Preparation Unit Objective 2

© A Very Good Teacher 2007 Parent Functions There are two parent functions on the TAKS test: 2, Ab2A LinearQuadratic y = x y = x² y axis is axis of symmetry Vertex at (0, 0) Opens up

© A Very Good Teacher 2007 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

© A Very Good Teacher 2007 Domain and Range, cont… Example of finding the Domain Domain: ____ < x ≤ ____ -32 2, Ab2B

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

© A Very Good Teacher 2007 Interpreting Graphs Pay attention to labels on x and y axes Identify the –slope (rate of change) –y-intercept (initial value) Keep in mind that step functions indicate a situation in which values must be whole numbers. 2, Ab2C You cannot sell half of a subscription!

© A Very Good Teacher 2007 Interpreting Graphs, cont… Example: Which statement is true for the graph below? 2, Ab2C A.Jiffy Joe will earn $2000 if he sells $1500 worth of merchandise B.Kent Karr will earn $2500 if he sells $6 worth of merchandise C.Cathy Camera will earn no money if she sells no merchandise D.Amanda Mann will earn $2000 if she sells $4000 worth of merchandise y-intercept is $ Slope is 500/2000 or 1/4 $6000!

© A Very Good Teacher 2007 Scatter Plots Correlation Positive Negative No 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 … x Per, each, dividend … Mean … ÷ Is or other verbs … Mean … = The goal is to turn a sentence into an equation. 2, 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. A=πr² So, you would look for the answer A = πr² 2, 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 2, Ab3B

© A Very Good Teacher 2007 Patterns, cont… Here’s an example: Figure# of squares Make a table 2, Ab3B

© 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. 2, Ab3B

© A Very Good Teacher 2007 Using symbols with AREA Often you will be asked to express the AREA of a figure using symbols Think about how area is calculated: l x w! Look for an answer that has 2 quantities multiplied Example: How can the area of the shaded rectangle be expressed in terms of x? 2, Ab3A 12 ft 17 ft x ft A.17 – 12x B. C. D. 12(17 – x) subtraction division Multiplication x

© A Very Good Teacher 2007 Using symbols with Percentages To find the sale price (50% off) subtract the percentage of discount from the original price –Example: John purchases a pair of shoes on sale for 30% off the regular price, p. Which expression represents the sale price of the shoes? A. p +.30pB. p -.30p C. 0.30p D p To find the total after sales tax, add the percentage of tax to the original price –Example: John purchases a pair of jeans for d dollars. If the sales tax rate is 7.5%, which expression represents the total cost of the jeans? A. 7.5d B. d C. d +.075d D. d -.075d 2, Ab3A

© A Very Good Teacher 2007 Writing expressions to get an even/odd output Example: Which expression will always produce an even integer? A. 4n + 1 B. 3n – 1 C. 4nD. -4n + 1 Use your calculator! Put each answer into and check the table 2, Ab3B A. 4n + 1B. 3n – 1C. 4nD. -4n + 1

© A Very Good Teacher 2007 Using the calculator to solve Quadratic Equations When the answers are numbers…. –Substitute each answer into each side of the equation until the sides are equal Example: The area of a rectangle is given by the equation 2w² + 7w = 39, where w is the width of the rectangle. What is the width of the rectangle? A. 4 B. 3.5 C.3 D.13 2, Ab4A

© A Very Good Teacher 2007 Using the calculator to solve Quadratic Equations, cont… 1.When the answers are algebraic expressions... (like 2x – 1 or x + 5) 2.Determine the relationship (A = l ▪ w) 3.Graph each side of the equation in 4.Find the graph that matches 2, Ab4A

© A Very Good Teacher 2007 Using the calculator to solve Quadratic Equations, cont… Example: The area of a rectangle is 3x² + 19x – 14, and the width is x + 7. Which expression best describes the rectangle’s length? A. (2x – 3) B. (3x – 2) C. (2x – 7) D. (3x – 7) 2, Ab4A A = length ▪ width 3x² + 19x – 14 = length ▪ (x + 7)

© A Very Good Teacher 2007 Simplifying Expressions Use properties to simplify completely Example: Simplify the algebraic expression 4(x – 3) + 3(x + 5). 2, Ab4B 1. Distribute 4x – x Combine like terms 7x+ 3

© A Very Good Teacher 2007 Simplifying Expressions Use the calculator to test for equivalence Example: Simplify the algebraic expression 4(x – 3) + 3(x + 5). 2, Ab4B A. 12x – 15 B. 7x + 3 C. 7x + 27 D. 4x Then type each answer until you get a result of “1”. This is the answer!

© A Very Good Teacher 2007 Important Vocabulary Linear Parent Function Quadratic Parent Function Domain Range Scatterplot Equivalent Geometric Sequence Area Percentage Even Number Odd Number Simplify y = x y = x² The set of x values The set of y values equal A sequence created by a series of shapes The amount of space occupied by a 2-D object A comparison of a number to a total of 100 Numbers that can be evenly divided by 2 {2, 4, 6, 8, 10, …} Numbers that cannot be evenly divided by 2 {1, 3, 5, 7, 9, …} To reduce an algebraic expression to its simplest form