Question

the number of women in the workforce for selected years from 1990 through 2040 is shown in the figure. complete parts (a) through (c). a. options for discrete/continuous not fully shown in ocr b. does the graph of y = w(x) shown in the bottom figure define the number of working women as a discrete or continuous function of the year? options for discrete/continuous c. is y = w(x) a reasonable model for the data points in the top graph? choose the correct answer below. a. no, because the graph of y = w(x) does not have the correct shape and does not appear to contain most or all of the data points on the scatterplot. b. yes, because the graph of y = w(x) has the same shape and appears to contain most or all of the data points on the scatterplot. c. yes, because the graph of y = w(x) appears to pass through maximum and minimum data points on the scatterplot. d. no, because the graph of y = w(x) does not appear to contain any of the correct data points on the scatterplot.

Explanation:

Step1: Analyze discrete - continuous nature for a

The data points in the top - graph are individual, separate values for specific years. So, it represents a discrete function.

Step2: Analyze discrete - continuous nature for b

The graph of \(y = W(x)\) in the bottom - figure is a smooth curve, which can take on any value within an interval. So, it represents a continuous function.

Step3: Evaluate the model for c

The graph of \(y = W(x)\) has the same general shape as the pattern of data points in the scatter - plot and appears to contain most or all of the data points. So, \(y = W(x)\) is a reasonable model.

Answer:

a. Discrete
b. Continuous
c. B. Yes, because the graph of \(y = W(x)\) has the same shape and appears to contain most or all of the data points on the scatterplot.