Table of values

Definition

A table of values lists pairs of numbers that satisfy a given function. It is used to plot the graph of the function by showing specific input-output relationships.

5 Must Know Facts For Your Next Test

1. A table of values helps in understanding the behavior of a function at specific points.
2. Each row in a table of values corresponds to an ordered pair $(x, f(x))$ where $x$ is the input and $f(x)$ is the output.
3. Tables are useful for visualizing functions that are difficult to graph directly from their equations.
4. They can be used to approximate solutions to equations by identifying where the function's values change sign.
5. When constructing a table, it is important to choose a range of $x$-values that captures key features like intercepts, maxima, and minima.

Review Questions

• How can you use a table of values to identify the intercepts of a function?
• Why might you choose certain $x$-values when creating a table for graphing?
• Explain how a table of values can help in approximating solutions to equations.

Related terms

Function: A relation between a set of inputs and allowable outputs where each input is related to exactly one output.

Graph: A visual representation of data points or mathematical functions on coordinate axes.

Intercept: $x$-intercepts are points where the graph crosses the x-axis ($y=0$) and $y$-intercepts are points where it crosses the y-axis ($x=0$).