Function Notation: Evaluating Functions 12/9/2015

Warm-Up If a function’s rule is f(x)=4x-6 find the output values for the table below -1 4 6 -10 -6 10 18

Recall what function notation means F(x) means “the output values for the function F with the input value x The output of the function F with the input value of 3 So, F(3) means: Remember: 1) A function has only one output for every input 2) A function can be named by many different letters (g(x), h(x), j(x)…)

Evaluating Functions A common question you will see is: “evaluate the function for a given value” In other words: “Find f (some number)” means “Find the output value for the function with some number as the input value. We can evaluate functions for given values using every form a function has {a mapping, graph, table of values, or rule in function notation.}

Evaluating a Function from a table When evaluating, or finding f(x), from a table use two steps. 1) Find the desired input value on the table 2) Record the corresponding output value as your answer

-98 54 In Out -2 54 23 3 -98 F(3) is ___________ F(-2) is ___________ Example: This table represent f(x) -98 In Out -2 54 23 3 -98 F(3) is ___________ 54 F(-2) is ___________

Evaluate a function from a rule To evaluate a function from a rule, also follow a two step process. 1) Substitute the given input value for ALL x’s in the rule 2) Simplify the expression using Order of Operations

Examples: 2) f(x) = 𝒙 𝟐 −𝟒𝒙 Find f(-2) 1) f(x) = 4x – 6 Find f(3) *substitute -2 for ALL x’s *substitute 3 for ALL x’s *Remember to use parenthesis for your substitution f(3) = 4(3) – 6 f(-2) = (−𝟐) 𝟐 −𝟒(−𝟐) *simplify f(-2) = 4−𝟒(−𝟐) f(3) = 12 - 6 f(-2) = 4+𝟖 f(3) = 6 f(-2) = 12

Picking the right function to use Sometimes, you will be given multiple function rules and be asked to find values of a specific function. In this case, it is important to be sure you are evaluating from the correct rule. Write the rule of the function you are being asked to evaluate. 2) Substitute the given input value. 3) Simplify using order of operations.

G(x) = 𝟓𝒙 𝒙−𝟐 G(4) = 𝟓(𝟒) 𝟒 −𝟐 G(4) = 𝟐𝟎 𝟒 −𝟐 G(4) = 𝟐𝟎 𝟐 G(4) =10 Example: F(x) = 3x – 4 G(x) = 𝟓𝒙 𝒙−𝟐 H(x) = 𝟏 𝒙−𝟒 Find G(4) Steps Work 1) 2) 3) G(x) = 𝟓𝒙 𝒙−𝟐 Write the function rule we need to use G(4) = 𝟓(𝟒) 𝟒 −𝟐 Substitute the given input value G(4) = 𝟐𝟎 𝟒 −𝟐 Simplify using order of operations G(4) = 𝟐𝟎 𝟐 G(4) =10

Identifying Domain and Range Domain is the set of input values listed least to greatest inside brackets Range is the set of output values listed least to greatest inside brackets Words that mean the same thing   Domain Range Input Output X-Value F(x) In Out

Example 1: Given a Domain and Function Find the range of f(x) = 3x – 2 if the domain is {-3, -2, 4, 5} How to do it: 1) Find the output for the 1st domain value given f(-3) = 3(-3) – 2 f(-3) = -9 – 2 f(-3) = -11 2) Repeat process for EACH domain value Find f(-2), f(4) and f(5) f(-2) = -8 f(4) = 10 f(5) = 13 3) Use proper notation to list range (outputs for each input) Range : {-11, -8, 10, 13}