math 1: algebra, geometry and statistics ms. sheppard ... · ... algebra, geometry and statistics...

Math 1: Algebra, Geometry and Statistics

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

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Function Notation Example: Use the following four functions. There may be more than one answer for each part. ! ! ! !"! !!!!!!!!!!!! ! ! !! ! !!!!!!!!!!!!!!!! ! ! !!! ! ! ! !!!!!!!!!!! ! ! !! ! ! For which function or functions will an input of 5 give an output of 21? ! ! ! !"! ! ! ! ! ! !"! !" ! ! ! !"

! ! ! !!!! ! ! ! ! ! !"! ! ! ! ! !"

! ! ! ! !! ! ! ! ! ! !" ! ! ! !"

! ! ! ! ! ! ! ! ! ! !"! ! ! ! ! !"

Both h(5) and k(5) equal 21, which means each of these two functions gives an output of 21 for an input of 5. Which function results in this input-output table? g(0)=10 h(0)=-4 j(0) = 25 k(0) = -4 Because only j(x) matches for an input of 0, I only have to try an input of 1 in j(x). j(1) = 5(1+5) = 5(6) = 30, so this table must be from j(x). :;3%&0<%%

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Input Output 0 25 1 30



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! ! ! !"! !!!!!!!!!!!! ! ! !! ! !!!!!!!!!!!!!!!! ! ! !!! ! ! ! !!!!!!!!!!! ! ! !! ! ! !

A= ;'()'!*+,)-($,!%3.+/-.!(,!-'(.!(,<+-=$+-<+-!-06/34!!

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!7.B3.$#>C%D3>'$#;>EF%%Use the functions ! ! ! !! ! !!!!!!! ! ! !!!

! !!!!!!! ! ! !!!!. Evaluate each expression.

Example: ! ! Plug 3 in for ! in the ! ! expression. Use parentheses. Then simplify the expression.

! ! ! ! ! ! ! ! ! ! !! ! ! ! ! !"

3. Use the functions below. Evaluate each expression. Be sure to simplify your answer fully.

! ! ! !!! !!!!!!!! ! ! ! ! !! !!!!!!! ! ! !

! ! !

a. ! ! b. Find ! !

Input Output 1 14 2 18



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e. !!!! f. !!!!!

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This is not a function because for the input of 2, you could add 2 and get 4 or add 3 and get 5. Because an input of 2 has more than one output, this is not a description of a function. !

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This is a function because each person has only one first name, and his or her first name has only one first letter. So each input has only one output.

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Domain (allowable x-values) and Domain Restrictions: The four basic functions (below) and variations of them have a domain of All Real Numbers ! ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! !!!!!!!!!!!!!!!!!!!!!! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! !!! Rational functions: The denominator cannot equal zero. Write the denominator is not equal to 0. Solve as if it were an equation. Example: ! ! ! !

!!!! !! ! ! ! ! (Add three to both sides) !! ! ! (Divide both sides by 2) !! ! !

! The domain of g(x) is all Real numbers except ! ! !

! Radical functions: The number under the square root cannot be negative. Write the expressions under the square root sign is ! !. Solve the inequality. Example: ! ! ! ! ! ! ! ! ! ! ! (Subtract three from both sides.) ! ! !! The domain of f(x) is all Real numbers where ! ! !! You Try:

5. Determine the domain of each function.

a. ! ! ! ! ! ! b. ! ! ! !!!!! c. ! ! ! !! ! !



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Domain and Range of Tables!The domain is the set of all inputs. The range is the set of all outputs. A table represents a function if no input has more than one output. Example: Find the Domain and Range of the table. Then determine if the table represents a function.

Domain: !! !!!!! !! !

Range: !!! !! !! !

The table does not represent a function because the input of 2 has more than one output (3 and !2)

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:;3%&0<F%7. Find the domain and range of the relation represented by the input-output table below. Then determine if the table represents a function.

Domain: Range: Is it a Function (explain):

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The domain of the graph is all Real number x-values greater than or equal to !2. Domain: all !! ! !!2!

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Input Output 0 2 2 3 -3 2 4 6 2 -2

Input Output 0 2 2 3 -3 2 4 6 5 -2

math 1: algebra, geometry and statistics ms. sheppard ... · ... algebra, geometry and statistics...

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