Tables connect inputs, outputs, and models

Each row keeps one input with its output

A table organizes paired values. If the problem gives $\left(1,5\right)$, then $x=1$ and $y=5$ belong on the same row. Entering the columns in different orders changes the relationship you are modeling.

1. In SAT Desmos, click +, then Table. You can also type table on a blank expression line.
2. Enter the inputs in $x_{1}$ and their matching outputs in $y_{1}$. Use Tab or the arrow keys to navigate the cells.
3. Use Zoom Fit beside the table if the points are outside your graph window.

Let a function calculate the second column

Define $f\left(x\right)=x^{2}+2$ on an expression line. In the table, change the second column heading from $y_{1}$ to $f\left(x_{1}\right)$. Desmos uses each input in the first column to calculate the matching output. These calculated cells are read-only.

For inputs −2, 0, and 3, the outputs are 6, 2, and 11. A table makes it easy to compare several values without retyping the rule.

$\displaystyle f\left(x\right)=x^{2}+2$

Define the rule on an expression line.

$\displaystyle f\left(x_{1}\right)$

Use this as the second column heading. The subscript identifies the first table's inputs. After typing x_1, press the right arrow to leave the subscript, then close the parenthesis.

Fit the model the question describes

A regression finds the coefficients of a model that fits paired data. After entering the points, press and hold the colored icon beside the second column heading (or right-click it) and choose Add Regression. Desmos adds a regression row that starts with Linear Regression; use its dropdown to choose Quadratic or Exponential when that model matches the question.

For $\left(1,5\right)$, $\left(2,7\right)$, and $\left(3,9\right)$, the fitted line is $y=2x+3$. Its slope is 2 and its y-intercept is 3. If the question asks for a prediction at $x=4$, substitute 4 to get 11.

A few points can fit more than one type of curve. Use the stated model or the context to choose. For measured data, a fitted curve estimates a trend; it does not make every point exact.

Keep practicing the connected skills