Absolute Value Equations(One Absolute Value) Objectives. Absolute Value Inequalities (> or ) Absolute Value Inequalities (< or )

Transcription

1 Section 5 Absolute Value Equations and Inequalities Solve Absolute Value Equations Solve Absolute Value Inequalities Involving < or Solve Absolute Value Inequalities Involving > or Absolute Value Equations(One Absolute Value) Solve each absolute value equation + 5 = + = Absolute Value Inequalities (< or ) Solve each absolute value inequalit Graph the solution set on a real number line Absolute Value Inequalities (> or ) Solve each absolute value inequalit Graph the solution set on a real number line 5 < >

2 Section Relations & Functions Understand Relations Find the Domain and Range of a Relation/Function Determine Whether a Relation Epressed as a Map, Ordered Pairs or a Graph Represents a Function Find the Value of a Function Domain and Range Find the domain and the range of the relation (,0) (, ) ( 0, ) Domain and Range Appling Concepts Find the domain and the range of the relation (,0) (,0) (,) (,) (,0) 5 The graph below shows the height, in feet, of a ball thrown straight up with an initial speed of 80 ft/sec from an initial height of of 5 feet after t seconds Determine the domain and range of the relation (,85) Height ( ft ) Time sec ( )

3 Copright 0, 00, 007 Pearson Education, Inc Relations as Functions A function is a relation in which each element in the domain (the inputs) corresponds to eactl one element in the range (the outputs) Relation - Not a Function This is a NOT function because there is an element in the domain (Bob) that does not correspond to eactl one element in the range (There is no wa that Bob can be 8 and 0 at the same time) Students Ages Bob John Bill Mark This is a function because each element in the domain (students) corresponds to eactl one element in the range (ages) 8 0 Students Bob John Bill Mark Ages 8 0 Vertical Line Test Vertical Line Test Vertical Line Test A set of points in the -plane is the graph of a function if and onl if ever vertical line intersects the graph in at most one point Function Not a Function Not a Function 7 Determine whether the graph represents a function a) b)

4 Vertical Line Test 8 Determine whether the graph represents a function a) (,) b) Finding the Value of a Function Find the value of each function 9 f ( ) = 5; f ( ) 0 h( t) = t t + ;h ( ) Section Linear Equations Find the & Intercepts Graph Vertical and Horizontal Lines Find the Slope of a Line Given Two Points Use the Point-Slope Form and Slope-Intercept 5 Graph a Line Find the Equation of a Line Given Two Points Graphing Graph each equation = =

5 Equation of a Line Write in standard form the equation of the line m = 5 ; (,0) Equation of a Line 5 Write the equation of the line that passes through the point (,) and is parallel to the line = Write in point-slope form the equation of the line that passes through the given points (,0) & (,5) Write the equation of the line that passes through the point (, ) and is perpendicular to the line = + Section Using Linear Models Write linear equations Make predictions from linear models Predicting with Linear Models A -mi cab ride costs $55 and a 5-mi cab ride costs $050 a Find a linear model for the given information (round to the nearest hundredth) Does the sign of the slope make sense? Eplain b How much does a 8-mi cab ride cost? c What is the maimum amount of miles, $8050 can afford? d Interpret the meaning of the slope and -intercept from part a

6 Predicting with Linear Models The table shows the winning times in the men's Olmpic 00-meter freestle swimming event for the ears 90-0 Use a graphing calculator a Make a scatter plot of the data and identif the trend line b Find linear model that best fits the data (round to four decimal places) Does the sign of the slope make sense? Eplain c Use the equation from part b to predict the time for the event in the ear 0 Year Time Section 5 Absolute Value Functions & Graphs Objective Graph absolute value functions Graphing Absolute Value Functions Graphing Absolute Value Functions Graph each absolute value equation Graph each absolute value equation f ( ) = f ( ) = + = f ( ) =