Type a function like y = 2x + 1 or x² − 2x − 3, choose where x starts, ends and how much it goes up each time, and get the full x/y table instantly. First and second differences reveal whether the pattern is linear, quadratic or exponential, and the points are plotted for you.
Last updated:
Use x, + − * / ^, parentheses, sqrt, cbrt, abs, sin, cos, tan, ln, log, exp, pi, e. Implicit multiplication works: 2x, 3(x+1).
Up to 1,000 rows.
Enter your values to see the result.
Advertisement
Advertisement
How to use the Table of Values Calculator
Enter the function using x, for example 3x - 5, x^2 + 1 or sqrt(x).
Set the start and end x-values for the table.
Choose the step: 1 gives whole numbers, 0.5 gives halves, and so on.
Press Generate table to fill in every y-value and draw the graph.
Copy or download the CSV to paste the table into a spreadsheet or homework.
How a table of values works
A function is a rule that turns each input x into one output y. To build its table, list the x-values from the start value in equal steps, substitute each into the rule and record y. For a step h, the x-values are x₀, x₀ + h, x₀ + 2h, … up to the end value. Each row (x, y) is one point on the graph of the function.
Example for y = x² − 2x − 3 with x from −2 to 4:
x
−2
−1
0
1
2
3
4
y
5
0
−3
−4
−3
0
5
1st difference
−5
−3
−1
1
3
5
2nd difference
2
2
2
2
2
The second differences are all 2, which confirms a quadratic. The y-values are symmetric around x = 1 (the vertex at (1, −4)), and y = 0 at x = −1 and x = 3, the two x-intercepts.
Reading patterns from differences
Function type
Example
What stays constant (equal x-steps)
Linear
y = 3x − 2
1st differences (equal to slope × step)
Quadratic
y = x² + 1
2nd differences (equal to 2a × step²)
Cubic
y = x³
3rd differences (6a × step³)
Exponential
y = 3 · 2ˣ
Ratio of consecutive y-values (base^step)
Tips for good tables
Always include x = 0: the row gives the y-intercept directly.
For a parabola y = ax² + bx + c, center the table on the vertex x = −b ÷ (2a) so the symmetry shows.
Use a small step near asymptotes (like x = 0 for 1/x) to see how fast the values grow.
For trig functions in degrees, a step of 30 or 45 lands on the familiar exact values.
If x-values are not evenly spaced, the differences no longer reveal the pattern; keep the step constant.
Frequently asked questions
What is a table of values?
A table of values lists chosen x-values (inputs) next to the y-values (outputs) a function gives for them. For y = 2x + 1, the x-values −1, 0, 1, 2 give y-values −1, 1, 3, 5. Plotting those pairs as points is the usual first step in graphing a function by hand.
How do I make a table of values for a function?
Pick a set of x-values, usually evenly spaced around 0, substitute each one into the rule, and work out y. For y = x² − 2x − 3 at x = 3: 9 − 6 − 3 = 0, so (3, 0) is on the graph. This calculator repeats that substitution for every x from your start to your end value in the step you choose.
What x-values should I pick?
Include 0 so you see the y-intercept, a few negative and positive values, and any x where something interesting happens, such as the vertex of a parabola or where the function crosses zero. A step of 1 works for most homework; use a smaller step such as 0.5 or 0.25 for curves that change quickly.
How can a table tell me if a function is linear or quadratic?
With evenly spaced x-values, a linear function has constant first differences (each y goes up or down by the same amount), a quadratic has constant second differences, and an exponential function has a constant ratio between consecutive y-values. The calculator checks all three and names the pattern.
Why does the table say undefined?
Some functions do not exist at certain x-values: 1/x at x = 0, sqrt(x) for negative x, or ln(x) for x ≤ 0. Those rows are marked undefined instead of showing a wrong number, and the graph leaves a gap there.
Can I use degrees for sin, cos and tan?
Yes. Set Trig angles in to Degrees and the table uses degree mode, so sin(30) = 0.5 and sin(90) = 1. In the default radian mode sin(x) expects radians, so x would go from 0 to about 6.283 for one full cycle.
How do I get the table into Excel or Google Sheets?
Press Copy table as CSV and paste into a spreadsheet, or use Download CSV to save a .csv file. Each row has x and y, plus the first and second differences when that option is on.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.