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Chapter 6: Problem 20

Plot the function \(f(x)=1 / \sqrt{x}\) over the range \(0.1 \leq x \leq 10.0\) using function tplot. Be sure to label your plot properly.

Short Answer

Expert verified
To plot the function \(f(x)=1 / \sqrt{x}\) over the range \(0.1 \leq x \leq 10.0\), use the 'tplot' function and label the plot appropriately. In 'R' programming language, the code would be: tplot(0.1:0.01:10, 1 / sqrt(0.1:0.01:10), type = 'l') title(main = 'Function plot of 1 / sqrt(x)', xlab = 'x', ylab = 'f(x)') This will generate a line graph of the function \(f(x)\) with the x-axis labeled as 'x', and the y-axis labeled as 'f(x)', and the title of the graph as 'Function plot of 1 / sqrt(x)'.

Step by step solution

01

Understand the Function

The function given here is \(f(x)=1 / \sqrt{x}\). This is a reciprocal square root function. In the positive range, it decreases as \(x\) increases because the larger the \(x\), the smaller the output of the function will be. Given the range \(0.1 \leq x \leq 10.0\), this behavior will be evident in the plot.
02

Use the function tplot to plot the function

To plot this function, the 'tplot' function needs to be used. In 'R' programming language, it would be like: tplot(0.1:0.01:10, 1 / sqrt(0.1:0.01:10), type = 'l') Here, "0.1:0.01:10" will generate the sequence of \(x\) from 0.1 to 10 with step size 0.01. The function "1 / sqrt(0.1:0.01:10)" will calculate the corresponding \(y\) values of the function \(f(x)\). The "type = 'l'" will plot a line graph.
03

Properly label the plot

To properly label any graph, a title and labels for both x and y axes are required. Here is how it can be done in 'R': title(main = 'Function plot of 1 / sqrt(x)', xlab = 'x', ylab = 'f(x)') In this code, "main" keyword is used to specify the title of the graph as 'Function plot of 1 / sqrt(x)', "xlab" is used to label the x-axis as 'x', and "ylab" is used to label the y-axis as 'f(x)'. Using these labels, the graph will be properly labeled and it will be clear what the graph is showing.

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