A function is defined as f(x) =xk , with k > 0 and x ≥ 0.(a) Sketch the graph of y = f(x)

To sketch the graph of y = f(x) = x^k, you need to follow these steps:

1. Identify the domain and range: Since x ≥ 0 and k > 0, the domain of the function is [0, ∞) and the range is also [0, ∞).

2. Identify the intercepts: The y-intercept is at (0,0) because f(0) = 0^k = 0. The x-intercept is also at (0,0).

3. Identify the end behavior: As x approaches ∞, y also approaches ∞ because raising a positive number to a positive power results in a larger positive number.

4. Sketch the graph: Start at the origin (0,0) and draw a curve that increases as it moves to the right. The curve should get steeper as x increases.

Remember, the exact shape of the graph will depend on the value of k. If k is 1, the graph is a straight line. If k is 2, the graph is a parabola. If k is between 0 and 1, the graph increases more slowly. If k is greater than 1, the graph increases more quickly.