By Dwight Chestnut Updated Aug 30, 2022
Pictures of mathematical functions are called graphs. Two‑dimensional graphs use an x‑axis and a y‑axis, while three‑dimensional graphs add a z‑axis. In a 2‑D graph, an equation takes the form y = f(x), indicating that the value of y changes as x varies. For instance, the linear function y = 2x produces the points (2, 4) and (6, 12). Plotting these relationships on a graph provides a visual representation of how x and y interact.
Draw a horizontal line on a sheet of paper and label it “x.” Divide the line into 10 equally spaced segments, marking each with a short vertical tick. Number the ticks from 1 to 10.
Draw a vertical line that intersects the horizontal line at its starting point. Label this line “y.” Divide it into 20 equally spaced segments, marking each with a short horizontal tick. Number the ticks from 1 to 20.
Plot the points of y = 2x. Begin with x = 1; then y = 2, so place a dot at (1, 2). Continue with x = 2 (y = 4), x = 3 (y = 6), and so on, up to x = 10 (y = 20). Each dot represents a solution pair.
Connect the dots with a straight line. The resulting line, rising from left to right, is the graph of the equation y = 2x.
Draw a horizontal line and label it “x.” Divide it into 10 equally spaced segments, marking each with a short vertical tick. Number the ticks from 0 to 10.
Draw a vertical line that intersects the horizontal line at its origin. This creates a positive half above the x‑axis and a negative half below. Divide the vertical line into 10 equal segments: five below (labeled 0 to –5) and five above (labeled 0 to 5). Add four intermediate ticks between 0 and 1 on both sides, labeled 0.2, 0.4, 0.6, and 0.8.
Plot the function y = sin(x). Using a calculator, evaluate sin(x) at integer values from 0 to 10. Place a dot at each (x, sin x) point: for example, (0, 0), (1, 0.84), (2, 0.91), and continue up to (10, –0.54). Each dot marks the corresponding y‑value for that x.
Join the dots with a smooth curve. The resulting wave oscillates between the positive and negative axes, illustrating the graph of y = sin(x).
