Graph the equations on one set of axes. \( f(x)=\sqrt{x} \) \( g(x)=\sqrt{x-4} \)

To graph the equations \( f(x) = \sqrt{x} \) and \( g(x) = \sqrt{x-4} \) on the same set of axes, we can follow these steps: 1. **Identify the Domain**: - For \( f(x) = \sqrt{x} \), the domain is \( x \geq 0 \). - For \( g(x) = \sqrt{x-4} \), the domain is \( x \geq 4 \) (since the expression under the square root must be non-negative). 2. **Calculate Key Points**: - For \( f(x) = \sqrt{x} \): - \( f(0) = \sqrt{0} = 0 \) - \( f(1) = \sqrt{1} = 1 \) - \( f(4) = \sqrt{4} = 2 \) - \( f(9) = \sqrt{9} = 3 \) - For \( g(x) = \sqrt{x-4} \): - \( g(4) = \sqrt{4-4} = 0 \) - \( g(5) = \sqrt{5-4} = 1 \) - \( g(8) = \sqrt{8-4} = 2 \) - \( g(9) = \sqrt{9-4} = \sqrt{5} \approx 2.24 \) 3. **Plot the Points**: - For \( f(x) \): - (0, 0) - (1, 1) - (4, 2) - (9, 3) - For \( g(x) \): - (4, 0) - (5, 1) - (8, 2) - (9, 2.24) 4. **Draw the Graphs**: - The graph of \( f(x) = \sqrt{x} \) starts at the origin (0,0) and curves upwards to the right. - The graph of \( g(x) = \sqrt{x-4} \) starts at the point (4,0) and also curves upwards to the right, but it is shifted to the right compared to \( f(x) \). 5. **Label the Axes**: - Make sure to label the x-axis and y-axis appropriately. ### Graph Representation While I can't create visual graphs directly, you can plot these points on graph paper or using graphing software. The key features to note are: - \( f(x) \) starts at (0,0) and continues to rise. - \( g(x) \) starts at (4,0) and rises from there. ### Summary - The graph of \( f(x) = \sqrt{x} \) is defined for \( x \geq 0 \). - The graph of \( g(x) = \sqrt{x-4} \) is defined for \( x \geq 4 \). - Both functions are increasing, but \( g(x) \) is shifted to the right by 4 units compared to \( f(x) \).