Evaluate your function
Use ^ for powers and y as the variable.
Example calculations
These values show common R-style notation.
| g(y) | y | Working | Result |
|---|---|---|---|
y^2 + 3*y - 4 | 5 | 25 + 15 − 4 | 36 |
sqrt(y) + log(y) | 9 | 3 + 2.1972 | 5.1972 |
log(y, 10) | 1000 | log base 10 of 1000 | 3 |
round(y/3, 2) | 10 | round 3.333... | 3.33 |
Formula used
The calculator evaluates the function after replacing the variable with your input:
g(y) = expression using y
For example, with g(y) = y^2 + 3*y - 4 and y = 5, the calculator uses 5^2 + 3×5 − 4 = 36. Exponents use ^. Trigonometric functions use radians, matching normal R behavior.
How to use this calculator
1. Enter g(y)
Type a formula such as y^2 - 6*y + 9. The optional g(y) = prefix is accepted.
2. Add a y value
Enter the number that replaces y. Negative values, decimals, and scientific notation are accepted.
3. Set output details
Choose decimal places and display style. Use scientific notation when values become extremely large or small.
4. Calculate
Select Calculate g(y). The result appears above this form with the normalized expression and substitution.
5. Review domains
Avoid invalid real values. For instance, sqrt(y) needs y at least zero.
6. Export or save
Download a CSV record or choose Print / Save PDF after a successful calculation.
Working with g(y) expressions in R
Understand the function first
A function maps an input to one output. Here, y is the input. The expression defines g(y). For example, g(y) = y^2 changes every y value into its square. Add terms when a rule needs more detail. A calculator helps confirm each substitution quickly.
Start by reading symbols in order. Parentheses group operations. Exponents apply before multiplication. Multiplication applies before addition and subtraction. This follows common mathematical order. Use explicit multiplication signs. Write 3*y, not 3y. That keeps your expression clear and readable.
Use R-style syntax carefully
R commonly uses ^ for exponents. The same notation works here. Write y^3 for y cubed. Use sqrt(y) for a square root. Use log(y) for a natural logarithm. For another base, write log(y, 10). Enter trigonometric functions as sin(y), cos(y), or tan(y).
Trigonometric values use radians. This matches standard R calculations. Convert degrees before calling a trig function. For 90 degrees, use sin(90*pi/180). Constants are also available. Use pi for π. Use e for Euler’s number. These details help formulas remain portable between practice work and R scripts.
Check a value step by step
Suppose g(y) = y^2 + 3*y − 4. Set y to 5. First, square five. This gives 25. Next, multiply three by five. This gives 15. Then add 25 and 15. Finally, subtract four. The final result is 36. The substitution line shows this same process.
Testing several y values reveals the function’s behavior. Try negative, zero, and positive inputs. A quadratic may decrease before rising. A logarithm changes only for positive inputs. A square root begins at zero for real values. Observing these rules can prevent incorrect assumptions.
Choose sensible precision
Precision affects display, not the internal rule. A result like 5.197224 may only need two decimals. Choose 5.20 for simple reporting. Keep more decimals during scientific work. Scientific notation is useful for extreme magnitudes. It makes small or large numbers easier to compare.
Do not round too early. Early rounding can change later calculations. Keep suitable decimals until the final answer. Then use the display selector. This calculator also provides CSV export. Save a calculation when you need a repeatable record. Use the print option when a PDF copy is more convenient.
Recognize common input problems
Some formulas have no real result for a chosen y. For example, sqrt(-4) is not real. Also, log(0) is undefined. Division requires a nonzero denominator. Check function domains before calculating. The calculator explains these issues rather than returning unsafe values.
Use commas only between function arguments. For example, round(y/3, 2) rounds to two places. Use parentheses around longer expressions. Write (y + 2)^2 when the complete sum is squared. Clear notation creates dependable results and simpler checking every time. Careful input makes your function checks faster, clearer, and easier to reproduce later in R.
Frequently asked questions
It names a function whose input is y. The formula tells the calculator how to transform that input into one output.
Yes. The calculator removes an opening g(y) = or g(y) <- label before evaluating the expression.
Use the caret. Write y^2 for y squared and (y + 1)^3 for a grouped cube.
Yes. Use log(y) for the natural logarithm. Use log(y, 10) for a base-10 result.
No. Trigonometric functions use radians, which matches R. Convert degrees with angle*pi/180 before using sin, cos, or tan.
Yes, when the formula accepts them. Negative inputs work for many expressions, but not real square roots or logarithms.
Use sqrt, abs, log, log10, sin, cos, tan, round, mean, sum, min, max, floor, and related listed functions.
Your input may be outside a real-number domain. Check for zero denominators, negative square roots, or nonpositive logarithm inputs.
Use commas only inside functions with multiple arguments, such as log(y, 10), mean(y, 4), or round(y, 2).
The display setting rounds the final shown result. It does not change how the original expression is evaluated internally.
After calculating, download the CSV file or use Print / Save PDF. Both options preserve the formula, input, and result.