Graphing Calculator

A graphing calculator draws the graph of a function so you can see its shape. Plot up to three functions of x over any range. The calculator marks x-intercepts, turning points and intersections, lists their coordinates, and leaves gaps where a function is undefined instead of joining across asymptotes.

Try:

How to use the graphing calculator

  1. Type one to three functions, such as x^2 - 4 and 2x + 1.
  2. Choose the x-range to show.
  3. Press Calculate to draw the graph and list its key points.

Formula

y=f(x)y = f(x)

Worked example: y = x² − 4 and y = 2x + 1

  • y₁ =: x^2 - 4
  • y₂ = (optional): 2x + 1
  • y₃ = (optional):
  • x from: -6
  • x to: 6

◐ Partly checked

y1=x2−4,y2=2x+1y_1 = x^{2} - 4,\quad y_2 = 2x + 1
y₁ = x^2 - 4: x-intercepts
-2, 2
y₁: y-intercept
-4
y₁: turning points
(0, -4) min
y₂ = 2x + 1: x-intercepts
-0.5
y₂: y-intercept
1
y₁ and y₂ intersect at
(-1.44949, -1.89898); (3.44949, 7.89898)
−6−4−2246−10102030(-1.45, -1.9)(3.45, 7.9)y₁y₂
Graph from x = -6 to 6. Dots mark x-intercepts, turning points and intersections.
Step-by-step working (2 steps)

  1. Plot the functions

    Each function is evaluated at hundreds of points across the range and joined up. Breaks are left where the function is undefined.

  2. Find key features

    x-intercepts and intersections are found where the sign changes, then narrowed down by repeated halving (bisection). Turning points are where the slope changes sign.

How this was checked
  • ✓ Each x-intercept of y₁ gives y ≈ 0 when substituted.
  • ✓ Each x-intercept of y₂ gives y ≈ 0 when substituted.
  • ✓ At each intersection both functions give the same y-value.

Features are found numerically within the chosen x-range and rounded.

Frequently asked questions

How do I find where two graphs meet?

Enter both functions. The calculator finds where y₁ − y₂ changes sign and narrows it down by repeated halving, then lists each intersection.

What functions can I plot?

Polynomials, fractions, roots, powers, exponentials, logarithms and trigonometric functions, using x as the variable.

Why are some answers labelled partly checked?

Intercepts and turning points are found numerically and rounded. Each one is still checked by substituting it back in.

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