Function Calculator
A function calculator should do more than plug in numbers. Type f(x) and this one evaluates it, builds a table of values, draws the graph, and marks where it crosses zero, where it turns and where it isn’t defined — with an optional g(x) for comparisons and compositions. Everything is calculated in your browser.
- Free to use
- No sign-up
- Runs in your browser
Function calculator
Use ^ for powers, * or a space-free product like 3x, and functions sin cos tan asin acos atan exp ln (log also means ln) sqrt abs; constants pi and e. Write x*sin(x), not xsin(x).
Function Practice Pack
Printable function worksheets with answer keys (evaluation, tables of values, composition, transformations), a function families reference card and coordinate graph paper.
- Evaluation worksheet (PDF/DOCX)
- Composition worksheet (PDF/DOCX)
- Families card (PDF)
- Graph paper (PDF)
Formats: PDF, DOCX. Instant download after payment (link valid 72 hours, up to 5 downloads). AI-assisted: the templates were drafted with AI help and reviewed and laid out before publishing.
$5.00 USD, one-time 4 files · about $1.25 each
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✓ Classroom use included
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Free sample: Composition Worksheet (PDF, 98 KB)
Full refund within 7 days — see the refund policy and license.
License: personal and classroom use. Teachers may print and photocopy these files for the students in their own classes, and share them in a password-protected class space (e.g. Google Classroom). Please do not resell, redistribute, or post the files on public websites. One purchase covers one teacher.
Free printables
Single sheets you can print right now, no sign-up. The full pack adds every sheet in one download plus the editable files.
Printable Coordinate Graph PaperWhat the calculator finds
| Result | How it is found |
|---|---|
| Values f(a) | Direct evaluation at each x you list |
| Table of values | Evaluation at every step across the range |
| Zeros | Sign changes of f across 800 sub-intervals, refined by bisection |
| Turning points | Sign changes of the exact derivative f′(x), refined by bisection |
| Gaps and jumps | Points where f is undefined or changes sign without passing through zero (as at a vertical asymptote) |
| Derivative | Symbolic differentiation with simplification |
| Compositions | f(g(a)) and g(f(a)) evaluated directly |
Zeros and turning points are searched only in the x-range you set, and features narrower than the sampling step can be missed — zoom in on a smaller range if you suspect one.
Worked example: f(x) = x³ − 3x + 1
On the range −3 to 3, the calculator finds three zeros, at x ≈ −1.879, 0.347, 1.532, a local maximum at (−1, 3) and a local minimum at (1, −1). The y-intercept is f(0) = 1 and the derivative is 3x² − 3, which is zero exactly at x = ±1 — matching the turning points. With g(x) = 2x − 1, the composition f(g(2)) = f(3) = 19 while g(f(2)) = g(3) = 5, a reminder that composition order matters.
Domain and range
The domain is the set of x-values where the function is defined. Common restrictions: division by zero (1/x is undefined at 0), square roots of negative numbers (sqrt(x) needs x ≥ 0) and logarithms of non-positive numbers (ln(x) needs x > 0). The range is the set of output values. The graph shows both at a glance: gaps in the curve mark domain restrictions, and the vertical extent shows the range over your chosen interval.
Common function families
| Family | Example | Shape |
|---|---|---|
| Linear | 2x − 1 | Straight line; slope 2, intercept −1 |
| Quadratic | x^2 − 4x + 3 | Parabola; zeros at 1 and 3, vertex at (2, −1) |
| Cubic | x^3 − 3x + 1 | S-shaped; up to two turning points |
| Exponential | 2^x or exp(x) | Rapid growth, always positive |
| Logarithmic | ln(x) | Slow growth, defined for x > 0 |
| Rational | 1/(x − 2) | Vertical asymptote at x = 2 |
| Trigonometric | sin(x) | Periodic wave, period 2π |
| Absolute value | abs(x − 1) | V shape with corner at x = 1 |
Transformations
- f(x) + k shifts the graph up by k; f(x) − k shifts it down.
- f(x − h) shifts it right by h; f(x + h) left by h.
- −f(x) reflects it in the x-axis; f(−x) reflects it in the y-axis.
- a·f(x) stretches it vertically by a factor a.
- f(b·x) compresses it horizontally by a factor b.
Put the original function in f and the transformed one in g to see both on the same axes.
Composition of functions
The composition f(g(x)) means “apply g first, then f”. In general f(g(x)) and g(f(x)) are different. The domain of f(g(x)) is limited both by g’s domain and by whether g’s outputs are in f’s domain: for f(x) = sqrt(x) and g(x) = x − 5, f(g(x)) = sqrt(x − 5) is only defined for x ≥ 5.
Even, odd and periodic functions
A function is even if f(−x) = f(x) for every x — its graph is symmetric about the y-axis, like x² or cos(x). It is odd if f(−x) = −f(x) — symmetric about the origin, like x³ or sin(x). Most functions are neither. To test, put your function in f and the same function with −x in place of x in g: if the curves coincide, f is even; if g is the mirror image of f in the x-axis, f is odd. A periodic function repeats at regular intervals: sin(x) and cos(x) repeat every 2π, tan(x) every π.
Checking answers from a textbook
- Evaluate at the exact value the question uses, including fractions like 1/3 or expressions like pi/4.
- If your answer and the calculator disagree slightly, check rounding — the calculator shows up to six decimal places.
- For zeros, confirm by evaluating f at the reported x; the result should be very close to 0.
- For a turning point, check that f′(x) = 0 there and look at the graph to see whether it is a maximum or minimum.
- Remember that trigonometric functions use radians here: sin(pi/2) = 1.
Tips for typing functions
- Powers: x^2, (x + 1)^3, 2^x.
- Multiply with * or by juxtaposition: 3x, 2(x + 1).
- Put functions in brackets: sin(2x), sqrt(x^2 + 1).
- Use x*sin(x), not xsin(x).
- Roots of negative numbers: x^(1/3) is undefined for negative x here; use −abs(x)^(1/3) on that side if needed.
Privacy
All calculations run in your browser.
Frequently asked questions
How do I find the zeros of a function?
Type f(x) and a range; the calculator finds sign changes and refines them.
Can it graph two functions?
Yes — enter g(x) to draw it on the same axes.
Does it show the derivative?
Yes, as a simplified formula.
Why is part of my graph missing?
The function is undefined there (e.g. square root of a negative number).
What does f(g(x)) mean?
Apply g first, then f to the result.
Is log base 10?
No — log and ln both mean the natural logarithm here; for base 10 use ln(x)/ln(10).
Does it use degrees or radians?
Radians. Convert degrees by multiplying by pi/180.
May I print and share these worksheets with my class?
License: personal and classroom use. Teachers may print and photocopy these files for the students in their own classes, and share them in a password-protected class space (e.g. Google Classroom). Please do not resell, redistribute, or post the files on public websites. One purchase covers one teacher.