How to evaluate f(x) (the core idea)

When you see a function written like f(x), it simply means “a formula that uses x.” Evaluating the function is a fancy way of saying: replace x with a specific number, and compute the result.

Example: Suppose f(x) = 2x^2 - 3x + 1. If you want f(4), you replace every x with 4:

• f(4) = 2·(4)^2 − 3·(4) + 1
• = 2·16 − 12 + 1
• = 32 − 12 + 1 = 21

That “plug in and simplify” pattern works for almost every function you’ll encounter in algebra and pre‑calc: polynomials, rationals, exponentials, logarithms, trig functions, and more. The only extra rule is: some functions have domain restrictions. For example, if your function is f(x)=1/(x-2), then x=2 is not allowed, because you would divide by zero. If your function uses a logarithm like ln(x), then x must be positive (because the natural log of 0 or a negative number is not real).

• Linear: f(x)=mx+b (straight line)
• Quadratic: f(x)=ax^2+bx+c (parabola)
• Polynomial: f(x)=a_n x^n+…+a_1 x+a_0
• Exponential: f(x)=a·b^x (growth/decay)
• Logarithmic: f(x)=a·log_b(x)+c (inverse of exponential)
• Rational: f(x)=P(x)/Q(x) (fractions of polynomials)
• Absolute value: f(x)=a·|x-h|+k (V-shape)

This calculator supports all of the above. You can type your function directly (best for most uses) or use the builder to generate the expression for you.

What happens when you press “Calculate f(x)”

Under the hood, the calculator does three steps: (1) builds a function expression, (2) validates it, and (3) evaluates it at your chosen x. If you also set table settings, it repeats the evaluation across a range of x values and prints a two‑column table (x, f(x)).

If you choose Type a function, the expression is whatever you type. If you choose Build a common function, the calculator constructs a valid expression automatically, like 3*x+2 for a linear function or (2*x+1)/(x-4) for a rational function.

The calculator only allows typical math characters and common function names (like sin, sqrt, ln, log). It also converts ^ into exponent notation and fills missing multiplication in cases like 2x → 2*x. If something looks off, you’ll see an error message.

Once the expression is cleaned, the calculator evaluates it using JavaScript’s math engine. If the result is not a real number (for example, division by zero, log of a negative, or an invalid expression), it will show “undefined” for that x value.

• Tables help you graph quickly (plot points, sketch curve).
• Tables help you check homework by testing multiple x values.
• Tables are easy to share (screenshots for study groups).

Function examples you can copy/paste

Try these examples to see how the calculator behaves with different function types. Each example is formatted the way most students naturally write functions. The tool will automatically insert missing multiplications where it can.

• f(x)=3x-7 (try x = 0, 1, 2)
• f(x)=-(1/2)x + 4

• f(x)=2x^2 - 3x + 1
• f(x)=x^3 - 6x^2 + 9x

• f(x)=(x+1)/(x-2) (note: x ≠ 2)
• f(x)=(2x-3)/(x^2+1)

• f(x)=2^x
• f(x)=3*(1.1^x) (growth model)
• f(x)=log(x) (base 10 log; x > 0)
• f(x)=ln(x) (natural log; x > 0)

• f(x)=sin(x) (x in radians)
• f(x)=cos(x)+1

Want a super‑clean table for graphing? Set Table Start to -5, End to 5, Step to 1 (defaults), then choose your function and hit calculate.

How to avoid common mistakes

If you mean “x divided by (x minus 2)”, write x/(x-2), not x/x-2. The second one means (x/x) − 2, which is different.

Write x^2 for “x squared”. This calculator converts it correctly. For multiplication, 2x is okay — it becomes 2*x.

• Rational: denominator cannot be 0.
• Log: the inside must be positive (x>0).
• Square root: for real outputs, inside must be ≥ 0.

If you’re sketching a graph, don’t trust one point. Generate at least 5–7 points. A single point can be correct while the overall shape is wrong. Tables make the curve obvious.

Frequently Asked Questions

• What is f(x) and how do I read it?

  “f(x)” is function notation. It means “the output of function f when the input is x.” If the function is f(x)=x^2, then f(3)=9 because 3² = 9.

• What formats are supported?

  You can use basic arithmetic (+, -, *, /), parentheses, powers with ^, and common functions like sqrt, abs, sin, cos, tan, ln, and log (base 10). Constants pi and e are supported too.

• Why do I get “undefined” for some x values?

  That usually means the function is not defined there. Common causes: dividing by 0, taking log(0), log(negative), or an expression error. Try a different x value or adjust the function.

• Are trig functions in degrees or radians?

  They use radians (like most math software). If you have degrees, convert first: radians = degrees × π/180. You can even type that directly: sin(30*pi/180).

• Can this calculator solve for x?

  This page is focused on evaluating and tabling functions (plugging in x). If you want to solve equations, use a Linear Equation Solver, Quadratic Solver, or a Graphing Calculator.

Function checkpoints (fast)

If you’re learning functions, these are the checkpoints teachers often test. You can use this calculator to verify each one by trying different x values and watching what happens.

• Domain: which x values are allowed?
• Range: what outputs are possible?
• Intercepts: where does the function hit the axes?
• Behavior: does it grow, decay, oscillate, or approach an asymptote?

Take a screenshot of your table, circle 2–3 “interesting points” (like zeros or peaks), and share it in your group chat. Someone will inevitably ask “how did you get that?”, and you’ll look like the person who actually understands functions.