Accurate Function Graph with Key Points
A correct, gridded graph of any function with intercepts, turning points and asymptotes marked.
Makes images - needs an image AI · Best tool: ChatGPT or Gemini (image)
✅ How to use this effectively
- 1. Open an image-capable AI chat.
- 2. Paste the prompt below.
- 3. Write your function in the INPUT line.
- 4. Send and wait for the graph.
- 5. Check the marked points, then download.
🔧 If it is not right, reply with this: If a point looks off, reply: "Re-solve the x-intercepts and turning point algebraically, list the coordinates, then redraw the graph to match."
THE PROMPT
ROLE: Act as a careful mathematics graphing assistant who plots functions accurately and labels every important feature. CONTEXT: I am a teacher making a graph for [CLASS/GRADE] under [BOARD or EXAM e.g. CBSE / ICSE / JEE]. I need a clean coordinate graph that students can read at a glance. YOUR TASK: 1. Take the function I give and plot it on labelled x and y axes with a light grid. 2. Mark and label these features where they exist: x-intercepts, y-intercept, turning points (maxima/minima), points of inflection, and any asymptotes (as dashed lines). 3. Write the function's equation neatly in a corner of the graph. 4. Choose a sensible x-range and y-range so all key features are visible. 5. Put coordinate values next to each marked point, like (2, 0). INPUT: Here is the function: [PASTE THE FUNCTION HERE, e.g. y = x^2 - 4x + 3]. Preferred x-range (optional): [e.g. -2 to 6]. HOW TO WORK IT OUT: First solve everything algebraically on the side: find intercepts by setting y = 0 and x = 0, find turning points using the derivative or vertex form, and find asymptotes by checking the domain. Then VERIFY by substituting two sample x-values back into the function and confirming the plotted curve passes through those y-values. Never guess the shape; never invent points. If the function has no real intercepts, state that clearly. OUTPUT FORMAT: 1. KEY POINTS (worked out): a short list of intercepts, turning points, asymptotes with coordinates. 2. THE GRAPH: one clean image with grid, labelled axes, marked points, and the equation shown. 3. ONE-LINE CHECK: the two substitution checks you used to confirm accuracy. RULES: Axes must be labelled x and y with arrows and a marked origin. The curve must visibly pass through every listed point. Use a plain white background. No clutter. SIGNATURE: Sign the bottom-right of every page with an elegant handwritten signature "[YOUR NAME]" with a small underline flourish.