4  Visualizing functions

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Reading questions

Reading question 4.1 What do we mean by the “input space” to a function (with a single input)?

The set of all possible values for the input.

The value of the input.

The typographical area between the open and close parentheses that follow a function name.

question id: 04-input-space

Reading question 4.2  

Figure 4.1: A graph of a function.

1. Figure fig-04-show-graph is a graph of a function; it shows the output corresponding to several different values in the input space. For the function shown, what is the output that corresponds to an input of six. (Pick the closest answer.)

0       2       -1      

question id: 04-show-graph-a

2. What is the graphics domain in Figure fig-04-show-graph? (Pick the closest answer)

0 to 8

2 to 6

1 to 7

none of these

question id: 04-show-graph-b

3. What is the mathematical domain of the function being shown in Figure fig-04-show-graph?

0 to 8

1 to 7

$-\mathrm{\infty }$ to $\mathrm{\infty }$

0 to $\mathrm{\infty }$

Can’t be determined from the graph.

question id: 04-show-graph-c

Reading question 4.3 Which axis represents the output in a function graph (like Figure fig-04-show-graph)?

x       y       z       none      

question id: 04-graph-axis

Reading question 4.4 Which axis represents the output in a contour plot?

x       y       z       none      

question id: 04-contour-axis

Reading question 4.5 What does domain() accomplish in drawing graphs with slice_plot() or contour_plot()?

It sets the domain of the function being graphed.

It sets the graphic domain, that is the region of input space shown in the graphic.

It isn’t used with slice_plot() or contour_plot().

question id: 04-domain-does

Reading question 4.6 What arguments does domain() take?

The name(s) of the function output(s)

The name(s) of the function input(s)

Either x or y or both, depending on how many inputs the function has.

question id: 04-domain-args

Reading question 4.7 In a contour plot, domain() takes two arguments. Why?

Reading question 4.8  

Figure 4.2

1. In Figure fig-04-colors, the contour plot has background shading on a spectrum from yellow to red. Explain when yellow is used and when red.

2. Which of these is the domain() used in Figure fig-04-colors?

domain(x = 0:5, y = 0:5)

domain(u = 0:5, v = 0:5)

domain(x = -5:5, y = -5:5)

domain(u = -5:5, v = -5:5)

question id: 04-colors-b

04-reading.rmarkdown

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