1 / 15

Graphing Exponential Functions

Section 4.3. Graphing Exponential Functions. Example. Graph by hand. Solution. List input–output pairs (see table) Input increases by 1 and output multiplies by 2 Plot these points (see next slide). Section 4.3. Slide 2. Graphing Exponential Functions with b > 1.

Download Presentation

Graphing Exponential Functions

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 4.3 Graphing Exponential Functions

  2. Example Graph by hand. Solution • List input–output pairs (see table) • Input increases by 1 and output multiplies by 2 • Plot these points (see next slide) Section 4.3 Slide 2 Graphing Exponential Functions with b > 1 Graphing Exponential Functions

  3. Solution Continued • Use graphing calculator to verify Section 4.3 Slide 3 Graphing Exponential Functions with b > 1 Graphing Exponential Functions

  4. Example Graph by hand. Solution • List input–output pairs (see table) • For example • (–1, 8) is a solution • x increases by 1, y is multiplied by ½ Section 4.3 Slide 4 Graphing Exponential Functions with 0< b < 1 Graphing Exponential Functions

  5. Solution Continued Section 4.3 Slide 5 Graphing Exponential Functions with 0< b < 1 Graphing Exponential Functions

  6. Property For an exponential function of the form y = abx, if the value of the independent variable increases by 1, the value of the dependent variable is multiplied by b. For the function , as the value of x increases by 1, the value of y is multiplied by 3 For the function , as the value of x increases by 1, the value of y is multiplied by 3/4 Illustration Section 4.3 Slide 6 Base Multiplier Property; Increase or Decreasing Property Base Multiplier Property

  7. Property Let , where a > 0. Then If b > 1, then the function f is increasing. We say that the function grows exponentially (left). If 0 < b < 1, then the function f is decreasing. We say that the function decays exponentially (right). Section 4.3 Slide 7 Increase or Decrease Property Base Multiplier Property

  8. Property For an exponential function of the form the y-intercept is (0, a). The function , the y-intercept is (0, 5) The function , the y-intercept is (0, 4) Illustration Section 4.3 Slide 8 Y-intercept of an Exponential Function Intercepts

  9. Warning Exponential function of the form , the y-intercept is not (0, b). By writing , we see that the y-intercept is (0, 1). For example, for , the y-intercept is (0, 1). Let 1. Find the y-intercept of f. Example Section 4.3 Slide 9 Intercepts and Graph of an Exponential Function Intercepts

  10. Solution is of the form , We know that the y-intercept is (0, a), or (0, 6). 2. Find the x-intercept of f. By base multiplier property, x increases by 1, y value multiplies by ½ Example Solution Section 4.3 Slide 10 Intercepts and Graph of an Exponential Function Intercepts

  11. Solution Continued No number of halvings will result in zero As x grows large, y gets closer to the x-axis Called horizontal asymptote 3. Graph f by hand. Example Section 4.3 Slide 11 Intercepts and Graph of an Exponential Function Intercepts

  12. Solution Plot solutions from the table • Verify on graphing calculator Section 4.3 Slide 12 Intercepts and Graph of an Exponential Function Intercepts

  13. Example • The graph of an exponential function f is shown. • Find f(2). • Blue arrow shows input of x = 2 leads to an output y = 8 • f(2) = 8 Solution Section 4.3 Slide 13 Finding Values of a Function from Its Graph Reflection Property

  14. Example • 2. Find x when f(x) = 2. • Red arrow shows output of y = –2 leads to an input x = 2 • x = –2 when f(x) = 2 Solution Section 4.3 Slide 14 Finding Values of a Function from Its Graph Reflection Property

  15. Example • 3. Find x when f(x) = 0. • Graphs of exponential functions get close to zero, but never reaches x-axis • No value of x where f(x) = 0 Solution Section 4.3 Slide 15 Finding Values of a Function from Its Graph Reflection Property

More Related