Function Graphing Calculator
Examples (tap one to load it):
Hover over the graph to trace a point, or drag to move the view. On a phone, tap the graph and use the buttons.
Function values:
Roots (x-intercepts):
Y-intercept:
Calculation:
Type up to three functions and see them drawn on the same plane. The calculator draws the axes with their scale, marks where each curve crosses the x-axis (the roots) and the y-axis, and lets you move along the curve with a point that shows (x, f(x)). Zoom with the buttons and move the view with the arrows or by dragging.
Below you will find how to write each function, worked examples and the most common questions.
How to use the function graphing calculator
Step 1: Type a function in f₁(x), for example x^2-4 or 2sin(x). Use ^ for powers, and you can write 2x instead of 2*x. Ready-made examples load with one tap.
Step 2: To compare, type another function in f₂ and a third in f₃. Each one gets its own color.
Step 3: Click Graph or press Enter. Use + and − to zoom and the arrows to move the view. Reset returns to the starting view.
Step 4: Move the cursor over the graph, type a value in Trace point or use the slider to read (x, f(x)). Roots and the y-intercept are marked on the graph and listed in the results.
How to write functions
Functions use the variable x. You can use addition, subtraction, multiplication, division, powers with ^, parentheses and these functions: sin, cos, tan, asin, acos, atan, sqrt, abs, ln, log and exp. The constants are pi and e. Angles in sin, cos and tan are in radians, and log is the base 10 logarithm.
| What you want | Type it like this | Value at x = 2 |
|---|---|---|
| x squared | x^2 | 4 |
| Multiply without writing the sign (2*x also works) | 2x | 4 |
| Fraction | 1/x | 0.5 |
| Fraction with parentheses | (x+1)/(x-1) | 3 |
| Square root | sqrt(x) | 1.414 |
| Absolute value | abs(x-5) | 3 |
| Natural logarithm | ln(x) | 0.6931 |
| Base 10 logarithm | log(x) | 0.301 |
| e to the power x | e^x | 7.389 |
| Sine of 2x (x in radians) | sin(2x) | -0.7568 |
| The number pi | pi*x | 6.283 |
If you type 1/2x, the calculator reads it as (1/2)·x. To divide by 2x, use parentheses: 1/(2x).
How roots and the y-intercept are found
A root of f is a value of x where f(x) = 0, so the curve touches or crosses the x-axis there. The calculator scans the current view, detects where the function changes sign and refines each result by bisection. The values are approximate and include only the roots inside the view. If you zoom in or out, the list updates.
| Root: f(x) = 0, y-intercept: (0, f(0)) |
The y-intercept is the point (0, f(0)). If the function is not defined at x = 0, as with 1/x, there is no y-intercept.
Examples of function graphs
Example 1: A parabola, f(x) = x^2-4
Roots in the starting view: x = -2, 2
Y-intercept: f(0) = -4
Trace point at x = 3: f(3) = 5
The curve opens upward and crosses the x-axis at two symmetric points.
Example 2: A wave, f(x) = 2sin(x)
Roots between x = -10 and x = 10 (7 points): -9.425, -6.283, -3.142, 0, 3.142, 6.283, 9.425
Y-intercept: f(0) = 0
The roots are the multiples of π (3.1416): the wave crosses the x-axis every π units. Its maximum height is 2.
Example 3: A function with an asymptote, f(x) = 1/x
Roots in the starting view: none
f(0) = undefined, because you cannot divide by 0
The curve has two branches, one on each side of the y-axis. The calculator does not join them, so you never see a false line crossing the asymptote.
Example 4: A cubic, f(x) = x^3-3x
Roots: x = -1.732, 0, 1.732
Y-intercept: f(0) = 0, and at x = 1: f(1) = -2
The three roots are 0 and ±√3 (about ±1.732). The curve rises, falls and rises again.
Frequently asked questions
How do I graph two functions at once?
Type one in f₁(x) and another in f₂(x). You can use up to three, and each is drawn in a different color. The results list the values, the roots and the y-intercept of each function separately.
Why is my graph cut off or full of gaps?
Because the function is not defined at those x values. For example, sqrt(x) exists only for x ≥ 0, ln(x) for x > 0, and 1/x does not exist at x = 0. The calculator leaves a gap instead of inventing a point. With tan(x) you will see breaks at the asymptotes.
Does sin(x) use degrees or radians?
Radians. To use degrees, type sin(x*pi/180). Then sin(90*pi/180) equals 1.
Are the roots exact?
They are approximate, with high precision. The calculator looks for them in the view you are seeing, so zoom out if you think distant roots are missing, or zoom in if two roots sit very close together.
Can I graph an equation like x^2 + y^2 = 1?
No, only functions of the form y = f(x). For a circle you can graph its two halves: sqrt(1-x^2) and -sqrt(1-x^2).
Learn more
- Graphs of linear functions
- Graphs of quadratic functions
- Graphs of trigonometric functions
- Transformations of graphs of functions
- Domain and range of exponential functions
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