Chapter 2

​​Chapter 2

Functions

Functions:

​A Function is a rule that assigns every input to an output.

To be a function every input (x-value) needs exactly one output (y-value)​

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​Types of Functions:

Sketching Functions:

​To sketch a function, we will take clues from the paragraph and draw a line on a graph. To do this, we need to keep track if our function is increasing or decreasing, and the duration of each interval.

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Ex: Jeanie was riding her bike home from school. She started off riding very fast for 5 minutes and then took a break for 2 minutes. Finally, she rode slowly home for 5 minutes. Sketch a function relating her distance from home and time.​

​A. The depth of the water in a pool decreased as the pool was drained.

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B. ​The temperature in the air decreases consistently from October to January.

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Functions in Tables

A Table Function is a way to directly show the relation between your inputs (x-values) and your outputs (y-values).

A table is a function if and only if the x values do not repeat.

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Ex:​

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Writing a function from a set of ordered pairs:

(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)​

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​Ex:

​(0, 1), (1, 3), (2, 9), (3, 27), (4, 81)

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Writing a function rule from a sentence:

30 more than one third of x is y.

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​5 less than the product of a number and 2 is 18.

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​Ex:

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​A: 10 more than 5 times a number is y.

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B: 11 less than a quotient of a number x and 3 is y.​

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Domain and Range:

​The domain is the set of all the first components of the ordered pairs, and the range is the set of all the second components of the ordered pairs. The domain is the set of all the first components. The range is the set of all the second components.

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Ex: {(0,0), (1,2), (2,3), (5,6)}

Domain:

Range:​

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​A. {(0, 0), (1, 1), (2, 8), (3, 27), (4, 64)}

​Domain:

Range:

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B. ​{(5, –4), (3, –5), (4, –3), (6, 4)}

Domain:

Range:​

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Find the range given the domain:

​If we are given the domain, that means we have all the x-values, but we need to find the y-values. To do this, we will plug in the inputs to get the outputs.

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E​x: f(x)=–3x+2; {–2, –2, 0, 1, 2}

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​A. f (x) = 4x + 1; {–4, –2, 0, 2, 4}

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B. f(x) = x³; {–1, –0.5, 0, 0.5, 1}​

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How to determine if a sequence is arithmetic

For a sequence to be arithmetic you must add the same number repeatedly.

EX: 1, 3, 5, 7, 9

​A. Determine if the sequence is arithmetic

4, 2, 0, -2, -4...


B. Determine if the sequence is arithmetic

1, 2, 4, 8, 16 ...