1 / 16

Section 2.1 What is a function?

Section 2.1 What is a function?. Objectives: To understand functions and function notation. To review domain. To understand how to evaluate functions and piecewise functions. To understand the difference quotient. Functions.

brynne-drake
Download Presentation

Section 2.1 What is a function?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 2.1What is a function? Objectives: To understand functions and function notation. To review domain. To understand how to evaluate functions and piecewise functions. To understand the difference quotient.

  2. Functions • A curve in the coordinate plane is the graph of a function if and only if no vertical line intersects the curve more than once. • Vertical Line Test – when given a graph, use this to verify if the curve is a function

  3. Ex 1. Use the vertical line test to determine if the following graphs are functions.

  4. Functions A function is a relationship between two variables such that each value of the first variable is paired with exactly one value of the second variable. Function notation: f(x) = y f(2) means evaluate the given function when x=2

  5. Ex 2. Given • Evaluate: • f(3) • f(-2) • f( )

  6. Getting Information from a Graph • The values of a function are represented by the height of its graph above the x-axis. • So, we can read off the values of a function from its graph.

  7. Ex. 3 Find the Values of a Function from a Graph The function T graphed here gives the temperature between noon and 6 P.M. at a certain weather station. • Find T(1), T(3), and T(5). • Which is larger, T(2) or T(4)?

  8. Class Work 1) a) Find f(50). b) Find f(100).

  9. Class Work 2.) Evaluate at the given values. • f(-2) b) f(4) c) f( ½ )

  10. Piecewise Functions A piecewise function is defined by different formulas on different parts of the domain.

  11. Ex 4. A cell phone plan costs $39 a month. • The plan includes 400 free minutes and charges 20¢ for each additional minute. • The monthly charges are a function of the number of minutes used, given by • Find C(100), C(400), and C(480)

  12. Class Work • Evaluate the piecewise functions at the indicated values. • f(-5) • f(3) • f(0) • f(1)

  13. Difference Quotient Ex 4. Evaluate f(x) = 3x – 1 at the following values. • f(a) • f(a + h)

  14. Class Work • Find the difference quotient, for the function:

  15. Use the function to evaluate the indicated expression and simplify. f(x) = 3x – 1 • f(2x) = • 2f(x) = • f(x2) = • (f(x))2=

  16. Pg.155 (13-27) odd, 29, 31, 35, 59, 60, 67, 68Pg. 167 (23-26, 55-60) all

More Related