Final answer:
Sketching the graph of the function f(x, y) = x^2 involves creating a table of x values and their corresponding y values as f(x) = x^2, plotting these points, and then drawing a smooth upward-opening parabola through the points.
Step-by-step explanation:
To sketch the graph of the function f(x, y) = x^2, we begin by understanding that this function describes a three-dimensional surface where the value of f(x, y) is solely dependent on the value of x, and not y. However, we can simplify the problem by understanding the graph of f(x) = x^2 in two dimensions.
Let's begin by creating a table of values for plotting data pairs. Choose several values for x, such as -2, -1, 0, 1, and 2. Compute the corresponding y values using the equation f(x) = x^2, yielding the pairs (-2, 4), (-1, 1), (0, 0), (1, 1), and (2, 4). Next, plot these points on a graph with appropriately scaled axes.
Using these points, draw a smooth curve connecting them to represent the parabola. Label the y-axis with f(x) and the x-axis with x. Remember that the graph of x^2 is a parabola that opens upwards with its vertex at the origin (0,0).
If you need to plot the function for a given range, such as 0 ≤ x ≤ 20, simply choose values within that range, compute the corresponding y values, and then sketch the graph accordingly, making sure to only draw the part of the graph where x lies between 0 and 20.