Problem 54 - College Algebra

Question

Graph each equation. $$y=-\frac{1}{x}\left(\text { Let } x=-2,-1,-\frac{1}{2},-\frac{1}{3}, \frac{1}{3}, \frac{1}{2}, 1, \text { and } 2 .\right)$$

Step-by-Step Solution

Answer

The graph of the function \(y=-\frac{1}{x}\) will appear as a hyperbola with appropriate points plotted for the given x-values.

Step 1: Identify the Equation

The given equation is \(y=-\frac{1}{x}\). It is important to understand that for a value \(x\neq0\), the function will give a valid output.

Step 2: Substitute values of x

To plot the graph, the corresponding y-values for the given x-values need to be computed by substituting each x-value into the equation. For example, for \(x=-2\), \(y=-\frac{1}{-2} = 0.5\) and for \(x=-1\), \(y=-\frac{1}{-1} = 1\).

Step 3: Plot the Points

Now that the y-values have been calculated, the points will be plotted on the coordinate plane. For example, the point for \(x=-2\) and \(y=0.5\) would be plotted at (-2,0.5).

Step 4: Draw the Curve

Finally, a curve will be drawn through all the plotted points. This should outline the shape of the hyperbola.