Question

In Exercises \(9-12,\) use a graph to find the zeros of the function. $$f(x)=2^{x}-5$$

Short answer

To find the exact zeros of the function by graphical method, we would closely observe the graph. The answer might not be extremely precise due to the limitations of visual estimation in the case of a graph.

Step-by-step solution

Understanding the Function

The given function to analyze is \(f(x) = 2^x - 5\). The zeros of this function are the values of x that satisfy the equation \(2^x - 5 = 0\). So, in order to find the zeros, one would need to solve for x in this equation.

Graphing the Function

To graph the function, one would typically use a graphing calculator or a plotting tool to get the desired visualization. The graph of \(f(x) = 2^x - 5\) would present an exponential curve shifted 5 units down on a typical coordinate grid.

Determining the Zeros from the Graph

The zero(s) of the function corresponds to the x-intercept(s) of the graph, or in other words, the point(s) where the graph cuts or touches the x-axis. A close observation would reveal the x-intercept for this function and thus identify the zero.