Function Notation and Making Predictions Section 2.3

Lehmann, Intermediate Algebra, 4ed Section 2.3 Rather than use an equation, table, graph, or words to refer to a function: name it If f is the name use to represent y: We refer to “ ” as functional notation We substitute for y in the equation does not mean f times x Slide 2 Introduction Function Notation Reads, “f of x”

Lehmann, Intermediate Algebra, 4ed Section 2.3 Substitute 4 for x in the equation : With function notation, the input is and output is Substitute 4 for x into the equation : mean input leads to an output of Slide 3 Introduction Function Notation

Lehmann, Intermediate Algebra, 4ed Section 2.3 Notice that is of the form The number is the value of y when x is 4 To find, we say that we evaluate the function at Evaluate Slide 4 Introduction/Evaluating a Function Function Notation Example

Lehmann, Intermediate Algebra, 4ed Section 2.3 Could have used “g” to name the function Common symbols are f, g, and h. Slide 5 Evaluating a Function Function Notation Solution

Lehmann, Intermediate Algebra, 4ed Section 2.3 Find given Slide 6 Evaluating Functions Function Notation Example Solution

Lehmann, Intermediate Algebra, 4ed Section 2.3 Find given Slide 7 Evaluating Functions Function Notation Example Solution

Lehmann, Intermediate Algebra, 4ed Section 2.3 Find given Slide 8 Evaluating Functions Function Notation Example Solution

Lehmann, Intermediate Algebra, 4ed Section 2.3 Some input–output pairs of a function are shown in the table. Find and Slide 9 Using a Table to Find an Output and an Input Function Notation Example Solution The input of leads to So, Inputs leading to are So, for,

Lehmann, Intermediate Algebra, 4ed Section 2.3 Let. Find Slide 10 Using An Equation to Find an Output and an Input Function Notation Example Solution

Lehmann, Intermediate Algebra, 4ed Section 2.3 Substitute and solve for x: Slide 11 Using An Equation to Find an Output and an Input Function Notation Solution Continued

Lehmann, Intermediate Algebra, 4ed Section 2.3 Verify solution using graphing calculator Use table in Ask mode Slide 12 Using An Equation to Find an Output and an Input Function Notation Graphing Calculator

Lehmann, Intermediate Algebra, 4ed Blue arrow shows that the input leads to output of So, Section 2.3 A graph of a function is sketched. Find refers to when We want y when Slide 13 Using a Graph to Find the Values of x and f(x) Function Notation Example Solution

Lehmann, Intermediate Algebra, 4ed The line contains the point (0, 1) So, Section 2.3 A graph of a function is sketched. Find refers to when We want y when Slide 14 Using a Graph to Find the Values of x and f(x) Function Notation Example Solution

Lehmann, Intermediate Algebra, 4ed Red arrow shows output originates from the input So, Section 2.3 A graph of a function is sketched. Find x when Want is the value of x when Slide 15 Using a Graph to Find the Values of x and f(x) Function Notation Example Solution

Lehmann, Intermediate Algebra, 4ed Output originates from the input So, Section 2.3 A graph of a function is sketched. Find x when Want is the value of x when Slide 16 Using a Graph to Find the Values of x and f(x) Function Notation Example Solution