Graphing Calculator

• Enter one function, such as x^2 - 4, or enter multiple functions on separate lines.
• Use the graph window controls or interact directly with the graph using wheel zoom and drag pan.
• Use Trace mode to inspect live ordered pairs on the graph.
• Use the Tangent tool to estimate a tangent line and slope behavior near the hovered point.
• Export the graph as an SVG for study notes, homework, or review.

• It reads each function and evaluates y-values across the chosen x-window.
• It plots points and connects smooth sections while avoiding undefined values and jumps.
• It estimates intercepts by checking where the graph crosses the axes.
• It identifies common function types such as linear, quadratic, rational, radical, exponential, logarithmic, trigonometric, and absolute value functions.
• It builds a table of values so students can connect the equation, graph, and numerical outputs.

Example 1 — Graph y = x² - 4

1. Enter x^2 - 4.
2. The y-intercept is found by evaluating f(0) = 0² - 4 = -4.
3. The x-intercepts happen where x² - 4 = 0.
4. Factor: (x - 2)(x + 2) = 0.
5. The graph crosses the x-axis at x = -2 and x = 2.
6. The graph is a parabola opening upward with vertex (0, -4).

Example 2 — Compare y = x² and y = (x - 2)² + 1

1. Enter both functions on separate lines: x^2 and (x - 2)^2 + 1.
2. The parent function y = x² has vertex (0, 0).
3. The function y = (x - 2)² + 1 is in vertex form.
4. The (x - 2) moves the graph right 2 units.
5. The +1 moves the graph up 1 unit.
6. So the new vertex is (2, 1).
7. This comparison helps students see how changing the equation transforms the graph visually.

Example 3 — Graph y = 1/x

1. Enter 1/x.
2. The function is undefined when x = 0 because division by zero is not allowed.
3. This creates a vertical asymptote at x = 0.
4. As x becomes very large or very small, the graph gets closer to y = 0.
5. This creates a horizontal asymptote at y = 0.
6. The graph appears in two separate branches, one in Quadrant I and one in Quadrant III.