Download 4.14.4 Graphing a Function Rule Find a function rule: Graph a

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