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Chapter 1: Problem 34

(a) use a graphing utility to graph the function and find the zeros of the function and (b) verify your results from part (a) algebraically. $$ f(x)=x(x-7) $$

Short Answer

Expert verified
The zeros of the function \( f(x) = x(x-7) \) are \( x = 0 \) and \( x = 7 \), as found both from the graph and algebraically.

Step by step solution

01

Use a graphing tool to plot the function

Use a graphing utility to plot the function \( f(x) = x(x-7) \). On the plotted graph, observe the points where the curve touches or crosses the x-axis.
02

Identify the zeros of the function from the graph

The zeros of the function are the x-values where the curve touches or crosses the x-axis. In this case, as per the graph, those should be at \( x = 0 \) and \( x = 7 \).
03

Verify the zeros algebraically

To verify the zeros algebraically, set the function \( f(x) = 0 \) and solve for \( x \). In other words, solve the equation \( x(x-7)=0 \). To solve this equation, either \( x=0 \) or \( x-7 = 0 \). If \( x-7 = 0 \), then \( x = 7 \). So the zeros of the function are \( x = 0 \) and \( x = 7 \). These results match those observed from the graph.

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