Begin by graphing $f(x)=2^{x}$. Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \[ g(x)=2^{x}-1 \] Which transformation is needed to graph the function $g(x)=2^{x}-1$ ? Choose the correct answer below. A. The graph of $f(x)=2^{x}$ should be shifted 1 unit downward. B. The graph of $f(x)=2^{x}$ should be shifted 1 unit upward. C. The graph of $f(x)=2^{x}$ should be shifted 1 unit to the right. D. The graph of $f(x)=2^{x}$ should be shifted 1 unit to the left.

Step 1 ：The function \(g(x)=2^{x}-1\) is a transformation of the function \(f(x)=2^{x}\).

Step 2 ：The transformation is a vertical shift of the graph of \(f(x)\) 1 unit downward.

Step 3 ：This is because the "-1" in the function \(g(x)\) subtracts 1 from each output value of the function \(f(x)\), which corresponds to moving the graph of \(f(x)\) down by 1 unit.

Step 4 ：So, the correct answer is: \(\boxed{\text{A. The graph of } f(x)=2^{x} \text{ should be shifted 1 unit downward.}}\)

Step 5 ：The domain of the function \(g(x)\) is the same as the domain of \(f(x)\), which is all real numbers.

Step 6 ：The range of \(g(x)\) is all real numbers less than -1, because the graph of \(f(x)\) is always above the x-axis, and shifting it down by 1 unit makes the graph of \(g(x)\) always above the line y=-1.

Step 7 ：The equation of the asymptote is y=-1, because that is the horizontal line that the graph of \(g(x)\) approaches as x goes to negative infinity.

Step 8 ：You can confirm these results by graphing the functions \(f(x)\) and \(g(x)\) on a graphing utility. The graph of \(f(x)\) is a curve that starts near the x-axis for negative x and increases rapidly for positive x. The graph of \(g(x)\) is the same curve, but shifted down by 1 unit.