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Function Notation and Making Predictions

Learn how to use function notation to evaluate and find values of a function. Understand how to substitute input values and solve for outputs using equations, tables, and graphs.

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Function Notation and Making Predictions

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  1. Section 2.3 Function Notation and Making Predictions

  2. 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 Reads, “f of x” Section 2.3 Slide 2 Introduction Function Notation

  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 Section 2.3 Slide 3 Introduction Function Notation

  4. 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 Example Section 2.3 Slide 4 Introduction/Evaluating a Function Function Notation

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

  6. Example Find given Solution Section 2.3 Slide 6 Evaluating Functions Function Notation

  7. Example Find given Solution Section 2.3 Slide 7 Evaluating Functions Function Notation

  8. Example Find given Solution Section 2.3 Slide 8 Evaluating Functions Function Notation

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

  10. Example Let . Find Solution Section 2.3 Slide 10 Using An Equation to Find an Output and an Input Function Notation

  11. Solution Continued Substitute and solve for x: Section 2.3 Slide 11 Using An Equation to Find an Output and an Input Function Notation

  12. Graphing Calculator Verify solution using graphing calculator Use table in Ask mode Section 2.3 Slide 12 Using An Equation to Find an Output and an Input Function Notation

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

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

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

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

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