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Transcript
4.14.4 Graphing a Function Rule function a relationship that pairs each input(x) value with one output(y) value linear function a function that makes a line when graphed nonlinear function a function that makes other shape when graphed discrete composed of distinct, isolated points continuous a graph that is unbroken Find a function rule: 4, 11, 18, 25 find difference (this number is next to x) what happens when you go backward? (this number is at end) Graph a function rule: make a table chose x values, plug in y values graph ordered pairs 4.4 Graphing a Function Rule 1) Graph the function rule y= 1/2x + 2 2) The function C=12.5h + 30 representing the total cost of renting a truck for h hours. Graph the function if the daily limit is 12 hours. 3) Megan buys eggs for $1.75 a carton. The cost is a function of the number of cartons bought. What is the graph of the function? Is the function discrete or continuos? 4) Write a function rule. x 0 1 2 3 y 2 1 4 7 4.5 Writing a Function Rule *Remember key words from Ch 1 when writing rule* Examples: Write a rule: the total cost C for p pounds of copper if each pound costs $3.57 the height in feet, f, of an object when you know the objects height h in inches Write a rule AND evaluate: A kennel charges $15 per day to board dogs. All dogs have to get a flea bath for $12. Write a rule for total cost n days plus a bath. How much does a 10 day stay cost? Does a 5 day stay cost 1/2 as much? Explain. Write a function rule for the area of a rectangle whose length is 3 in. more than the width. What is the area when the width is 7 in? 4.6 Formalizing Relations and Functions relation: a pairing of numbers domain: xvalues in relation range: yvalues in relation vertical line test: if any vertical line passes through 2 points on a relation at the same time, it's NOT a function function notation: f(x)= something (f(x) is the same as y) Mapping Example: (2,2) (0,6) (5,1) (4,3) 2 0 4 5 1 2 3 6 *all numbers are in order, separated x & y *if there are 2 of the same x's going to different y's, its NOT a function 4.6 Formalizing Relations and Functions Identify the domain and range of the relation. Use a mapping diagram to determine whether the relation is a function. 1) {(3, 1), (0,2), (1,1), (2,4)} 2) {4, 6), (5,1), (7,2), (5,2)} Use the vertical line test to determine if it's a function. Find the range of each function for the given domain. 4) f(x) = 3x 2 domain: {1, 2, 3} 5) You buy chips for $2.50 per package and a giftcard worth $10. f(x)=2.50x 10 represents your spending. How much do you pay if you buy 5 bags of chips? 4.7 Arithmetic Sequences A(n) = A(1) + (n1)d common difference: the difference between each term *multiply this* first term term you're looking for sequence: a ordered list of numbers that forms a pattern term: each number in a sequence arithmetic sequence: the difference between the terms is constant **MEMORIZE the formula!!** 4.7 Arithmetic Sequences Describe a pattern in each sequence. Find the next two terms. 1) 3, 11, 19, 27... 2) 3, 6, 12, 24... Tell whether the sequence is arithmetic. If it is, identify the common difference. 3) 1, 7, 14, 21... 4) 11, 20, 29, 38... Find the second, fourth, and eleventh terms of the sequence described by each explicit formula. 5) A(n)=3 + (n1)5