1 / 7

2.2

2.2. DOMAIN AND RANGE. Definitions of Domain and Range. If Q = f ( t ), then • the domain of f is the set of input values, t, which yield an output value. • the range of f is the corresponding set of output values, Q. Choosing Realistic Domains and Ranges. Example 2

grazia
Télécharger la présentation

2.2

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. 2.2 DOMAIN AND RANGE

  2. Definitions of Domain and Range If Q = f(t), then • the domain of f is the set of input values, t, which yield an output value. • the range of f is the corresponding set of output values, Q.

  3. Choosing Realistic Domains and Ranges Example 2 Algebraically speaking, the formula T = ¼ R + 40 can be used for all values of R. However, if we use this formula to represent the temperature, T , as a function of a cricket’s chirp rate, R, as we did in Chapter 1, some values of R cannot be used. For example, it does not make sense to talk about a negative chirp rate. Also, there is some maximum chirp rate Rmax that no cricket can physically exceed. The domain is 0 ≤ R ≤ Rmax The range of the cricket function is also restricted. Since the chirp rate is nonnegative, the smallest value of T occurs when R = 0. This happens at T = 40. On the other hand, if the temperature gets too hot, the cricket will not be able to keep chirping faster, Tmax=¼ Rmax+40. The range is 40 ≤ T≤ Tmax

  4. Using a Graph to Find the Domain and Range of a Function A good way to estimate the domain and range of a function is to examine its graph. • The domain is the set of input values on the horizontal axis which give rise to a point on the graph; • The range is the corresponding set of output values on the vertical axis.

  5. Using a Graph to Find the Domain and Range of a Function h height of sunflower (cm) Analysis of Graph for Example 3 A sunflower plant is measured every day t, for t ≥ 0. The height, h(t) in cm, of the plant can be modeled by using the logistic function Solution • The domain is all t ≥ 0. However if we consider the maximum life of a sunflower as T, the domain is 0 ≤ t ≤ T • To find the range, notice that the smallest value of h occurs at t = 0. Evaluating gives h(0) = 10.4 cm. This means that the plant was 10.4 cm high when it was first measured on day t = 0. Tracing along the graph, h(t) increases. As t-values get large, h(t)-values approach, but never reach, 260. This suggests that the range is 10.4 ≤ h(t) < 260 h(t) t time (days)

  6. Using a Formula to Find the Domain and Range of a Function Example 4 State the domain and range of g, where g(x) = 1/x.

  7. Solution The domain is all real numbers except those which do not yield an output value. The expression 1/x is defined for any real number x except 0 (division by 0 is undefined). Therefore, Domain: all real x, x≠ 0. The range is all real numbers that the formula can return as output values. It is not possible for g(x) to equal zero, since 1 divided by a real number is never zero. All real numbers except 0 are possible output values, since all nonzero real numbers have reciprocals. Therefore, Range: all real values, g(x) ≠ 0.

More Related