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Functions

Functions. Algebra: 5.01/ functions 8.f.1,.2,.3 Define evaluate and compare functions - Translate various representations of functions and identify relations as linear or nonlinear. Vocabulary.

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Functions

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  1. Functions Algebra: 5.01/ functions 8.f.1,.2,.3 Define evaluate and compare functions -Translate various representations of functions and identify relations as linear or nonlinear

  2. Vocabulary Function- A rule that relates two quantities so that each input value corresponds to exactly one output value Input-The value substituted into an expression or function Output- The value that results from the substitution of a given input into an expression or function

  3. Vocabulary • Domain- The set of all possible input values • Range- The set of all possible output values • Function Notation- The notation used to describe a function. • Ex. y=3x2 f(x)= 3x2 • f(x) is read “f of x”

  4. Representation Tables Graphs Equations

  5. Representations • Make a table of inputs and outputs • Use the table to make a graph

  6. Identify a Function To determine if a relationship is a function, verify that each input has exactly ONE output One x value has one y value. This IS a Function!

  7. Identify a Function The input x=0 has two outputs, y = 3 and y = -3. Other x values also have more than one y value. The relationship is NOT a function!

  8. Identify a Function Make an input-output table and use it to graph y=x2 Each input, x, has only one output, y. The relationship IS a function.

  9. Function Notation The output value of the function, f that corresponds to the input value x is written, f(x) The expression f(x) means “the rule of f applied to the value of x. Not f multiplied by x

  10. Function Notation • y= x2 = f(x)=x2 • The output y is the rule of f applied to x • F(1) = 12= 1 • F(1) means evaluate f(x) for x = 1

  11. Evaluating Functions For each function, find f(0), f(2), and f(-1) Y= 2x - 1 f(x)= 2x - 1 f(0)= 2(0) – 1 =-1 3 f(2) = 2(2) – 1 = f (-1)= 2(-1) – 1 = -3

  12. Evaluating Functions Read the graph to find y for each x f(x)= y f(0)= -4 f(2) = -2 f (-1)= -5

  13. Evaluating Functions Read the table to find y for each x f(x)= y f(0)= 2 f(2) = 8 f (-1)= -1

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