Algebra 1: Chapter 4 Notes

Transcription

1 Algebra : Chapter Notes Notes #: Sections. and. Section.: Graphing on the Coordinate Plane A written as (, ) represents a dot on the coordinate plane; ou just need to find where the point goes. The first number, or the -, is the horizontal (left/right) distance. The second number, or the - is the vertical (up/down) distance. The Coordinate Plane x Example: (, ) Graph and label each point on the coordinate plane:.) A (-, ).) B (, -).) C (, ).) D (, 0) Name the coordinates of the following points:.) E.) F The coordinate plane is split up into sections, also called. We can describe where a point is b naming its quadrant. In which quadrant is each point located?.) (-, ).) (.,.).) (., -) 0.) The point units to the left of the -axis and units below the x-axis..) The point units to the right of the -axis and units above the x-axis.

2 Section.: Relations and Functions Vocabular: Relation: an set of (or ) Domain: the set of of a relation written in { }. The domain values are often called the. Range: the set of of a relation written in { }. The domain values are often called the. Function: a relation in which each is paired with a unique. Meaning, in a function, the - coordinate should not be repeated. Table: another wa to list a set of points Find the domain and range of each relation. Is the relation a function?.) {(, ), (, 0), (, ), (, )}.) {(, ), (, ), (, ), (, )}.) x A relation is often called a because we can map x-values to -values. Determine whether each relation is a function: (it might help to write as points first).) Domain Range.) Domain Range.) Domain Range.) Domain Range

3 How can we determine whether a relation is a function if we onl look at its graph?.) Let s write a relation that is NOT a function. We ll graph the points below: 0.) Let s write a relation that IS a function. We ll graph the points below: x x What do ou notice about the coordinates that make this relation NOT a function? From a graph, to test whether a relation is a function, we use the test. - If an vertical line touches the relation more than once then it is a function - If all vertical lines touch the relation zero or one time, then it a function Which of the following are functions?.) x ) x

4 .) x ) x You need to know how to find the domain and range of a graphed relation: Domain: Read the graph from to. What -values are represented on the graph? Range: Read the graph from to. What -values are represented on the graph? For #, find the domain and range of each relation. Is it a function?.).) x ) x x.) x

5 Review Topics: Distance/Rate/Time Problems.) Two cars leave town at the same time heading in the same direction. One car travels at 0mph and the other travels at 0mph. After how man hours will the be 0 miles apart? 0.) Lisa drives into the cit to bu a software program at a computer store. Because of traffic, she averages onl mi/h. On her drive home she averages mi/h. If the total travel time is hours, how long does it take her to drive to the store?.) Two cars leave town at the same time going in opposite directions. One of them travels 0mph and the other travels at 0mph. In how man hours will the be 0 miles apart?

6 Notes #: Sections. and. Section.: Using Function Rules and Tables to Graph A is a rule, or an that describes a function. A function s domain, or, determines its range, or. Functions are often written in. Instead of, we use terms such as f(x), g(x), h(x) because the -value on the x. Find the indicated outputs for these functions: The number in the parentheses is x. Plug this number in for x. This is the input. The answer is our output. Write as a point or in function notation..) f(x)= x + ; find f(), f(-), and f (0).) g(x)= -x ; find g(), g(), and g(0) x f(x)= x + (x, ) Find the range of each function for the domain {-, 0, }.) h(x) = -x + x.) = x

7 Functions can be modeled using rules, tables, or graphs. The inputs are values of the variable and the outputs are corresponding values of the variable. Model each rule with a table of values and a graph.) f(x)= -x What is the domain of this function? What is the range of this function?.) = x What is the domain of this function? What is the range of this function?.) g(x) = x What is the domain of this function? What is the range of this function? x x x

8 Section.: Writing Function Rules You can write a rule for a function b analzing a table of values and looking for a pattern. You will ask ourself What can I do to the x-value to get the -value? You need to be sure that the pattern works for all points of the function. Also, be sure to write our answer in. Examples: x f(x) x f(x) You can also write a rule for a function that is modeled b a sentence or word problem. Be sure to look for ke words for clues. Reminder: sum ( ), more than ( ), less than ( ), product ( ), quotient ( ), difference ( ) Examples: the total cost t(c) of c pounds of apples if each pound of apples costs $0.0 the width w(l) of a picture that is three cm more than the length l Write a function rule for each table or situation:.).) x f(x) x f(x) ) the distance d(t) traveled at miles per hour in t hours.) the value v(d) of a pile of d dimes.) a worker s earnings e(h) for h hours of work at $.0 per hour.) the volume v(e) of a cube when ou know the length of an edge e

9 Review Topics: Mixture Problems and Properties of Real Numbers.) Raisins cost $ per pound and nuts cost $ per pound. How man pounds of each should ou use to make a 0-lb mixture that costs $ per pound?.) A chemist has one solution that is 0% acid and another solution that is 0% acid. How man liters of each solution does the chemist need to make 00 liters of a solution that is % acid? Name the propert that is illustrated below. (Identit, Inverse, Commutative, Associative, Distributive, Mult Prop of Zero)..) + = +.) ()() =.) x + = (x + ).) ( ) = ( ) 0.) ( ) = ( ).) 0 + (-m) = -m.) 0 = 0.) -x + x = 0.).

10 Notes #: Section. and Review Topics Section.: Inductive and Deductive Reasoning Inductive Reasoning: You use inductive reasoning when ou use or to make a conclusion. This conclusion is probabl but not necessaril true. Look for a pattern and use inductive reasoning to predict the next two numbers in each sequence:.) -,,,,,.),,,,,.),,,,, Deductive Reasoning: You use deductive reasoning when ou follow or to make a conclusion. This conclusion must be true. Accept the two statements as given information. State a conclusion based on deductive reasoning. If no conclusion can be reached, write none..) Mr. McCullough is taller than Mr. Chen. Mr. Chen is taller than Mrs. Spragg..) Mr. Renolds is taller than Mrs. Spragg. Mr. Brown is taller than Mrs. Spragg..) All math teachers eat soup. Mr. Jones eats soup..) All math teachers eat soup. Mr. Sha is a math teacher. Identif whether the reasoning process used below is deductive or inductive:.) Napoleon noticed that Kip had nachos for lunch for the past three Tuesdas. Napoleon decides that Kip alwas has nachos for lunch on Tuesdas..) Miss Krabappel tells Bart that if he doesn t do his homework assignment that he will earn a zero. Bart does not do his homework. Bart concludes that he will get a zero on that assignment. 0.) Han Solo knows that Yoda is more powerful than Darth Vader. Han also knows that Darth Vader is more powerful than Leia. Han concludes that Yoda must be more powerful than Leia.

11 Review Topics: Solving Equations Solve for the variable. If it is an inequalit, please include a graph with our solution:.) x.) x.) (m +) =.) x.) ( + ) = + ( ).) w w.) g...) - < x.) v + < or -v + < 0.) w.).) c