Composition of Functions

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Presentation transcript:

Composition of Functions Skill Check Composition of Functions (After HW Check)

Go over homework

Composition of Functions Skill Check Composition of Functions

Sequences A sequence is a function whose domain is a set of consecutive whole numbers. So the domain in any sequence is {1,2,3,4…} The values in the range are called the terms of the sequence. A sequence can be specified by an equation or a rule.

Arithmetic Sequence A sequence of terms that have a common difference between them

Determine if the sequence is arithmetic. Example: -22, -15, -8, -1, … Arithmetic d = 7

Determine if the sequence is arithmetic. Example: ½, ¼, 1/8, 1/16, … Not Arithmetic

Determine if the sequence is arithmetic. Example: 7, 4, 1, -2, -5 Arithmetic d = -3

Explicit Formula Formula used to find the nth term of a sequence

Explicit Formula for Arithmetic Sequence Before: After:

Find the common difference, the explicit formula (check your answer), and the tenth term. 3, 9, 15, 21, … d = 6 an = 6n – 3 a10 = 57

Find the common difference, the explicit formula (check your answer), and the twentieth term. Another way to look at it: What do the pieces mean? 7, 4, 1, -2, … What would it look like if you drew it? What would the slope be? How would you get the y-intercept? So: The difference between the numbers. In this case, -3. Look at the number that would be BEFORE the first. In this case, 10 would come BEFORE 7.

Find the common difference, the explicit formula (check your answer), and the sixteenth term. 17, 21, 25, …

Applications The marching band has 14 marchers in the front row, 16 in the second row, 20 in the fourth row, and so on. How many marchers are in the 15th row?

Applications Several friends want to go on a rafting trip. The cost of the trip per person is in the chart. How much would it cost for 9 people to go? Passengers 1 2 3 4 Cost $75 $100 $125 $150

Explicit vs. Recursive Notation

Explicit vs. Recursive Notation Explicit Notation – Lets you find any term immediately without using any others Recursive Notation – Defines a given term based on the previous term

(This one doesn’t simplify) Arithmetic Sequences Explicit Notation: Recursive Notation: (This one doesn’t simplify)

Convert from explicit to recursive: Write out the first 3 terms Find the difference and the first term Plug them into the formula 11, 14, 17,… d = 3; a1 = 11

Convert from recursive to explicit: Write out the first 3 terms Find the slope and y-intercept (go back one for a0) Plug them into the slope-intercept formula 5, 2, -1,… m = -3; b = 8 (which would be before the 5)

Classwork & Homework Worksheets