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Chapter 1: Problem 23

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=4+(1 / x)$$

Short Answer

Expert verified
The graph of the function \(f(x) = 4 + (1 / x)\) is a hyperbola, shifted 4 units upwards. At \(x=0\), the function is undefined, and as \(x\) approaches 0, \(f(x)\) tends towards negative and positive infinity.

Step by step solution

01

Understand the Function

The function given here is \(f(x) = 4 + (1 / x)\). This function is composed of a constant, \(4\), and a reciprocal function, \((1 / x)\). The constant \(4\) will vertically shift the graph by 4 units upwards. The reciprocal function, \((1 / x)\), will yield a hyperbola.
02

Determine the Viewing Window

The appropriate viewing window will need to show all significant aspects of the function鈥檚 graph including any asymptotes, zeros, or shifts. Given this function, a good viewing window might be \(x\) from \(-10\) to \(10\) and \(y\) from \(-10\) to \(10\). This will allow enough view on all sides to see the behavior of the function.
03

Graph the Function

Input the function into the graphing utility and set the viewing window. The graph shows that \(f(x)\) is a hyperbola that has been shifted 4 units upward. As \(x\) approaches 0 from the left or right, \(f(x)\) approaches negative or positive infinity, respectively. The function does not exist at \(x=0\) as it will result in division by zero.

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