📚 Practice With Worksheets
Practice identifying functions, using the vertical line test, and completing function tables from a given rule.
▶️ Learn With Videos
See how functions model geometric relationships and how sets of points can be analyzed from tables, equations, and graphs.
🛠️ How to Use This Tool
Choose Linear, Exponential, or Quadratic, then select New Function to generate another rule from that family.
Enter an input value for \(x\) and select Plot Point to add the corresponding output, ordered pair, and graph point. Use Add Sample Points to build a seven-row function table automatically.
Zoom, pan, or center the graph to examine its shape. Remove individual table rows or clear the table whenever you want to test a different set of inputs.
🧠 Things to Notice
Each table row, ordered pair, and plotted point represents the same input-output relationship described by the function rule.
Linear graphs have a constant rate of change, exponential graphs change by a constant multiplicative factor, and quadratic graphs form parabolas.
Look for how equal changes in \(x\) affect the outputs. The pattern of change helps distinguish one function family from another.
📘 Vocabulary
Function: A relationship that assigns each input exactly one output.
Input: The value placed into a function, usually represented by \(x\).
Output: The value produced by a function, usually represented by \(y\) or \(f(x)\).
Function Rule: An equation or process that describes how each input is changed into an output.
Function Table: A table that organizes corresponding input and output values.
Ordered Pair: A coordinate pair written as \((x,y)\) that represents an input and its output.
Linear Function: A function with a constant rate of change whose graph is a straight line.
Exponential Function: A function in which the variable appears in the exponent and values change by repeated multiplication.
Quadratic Function: A function containing a squared variable term whose graph is a parabola.
Parabola: The curved graph produced by a quadratic function.
Rate of Change: A comparison of how much the output changes when the input changes.
Coordinate Plane: A grid formed by perpendicular number lines used to plot ordered pairs.
📐 Connecting Function Representations
A function rule determines the output associated with each input. Substituting an input value into the rule produces one ordered pair.
\(x \longrightarrow f(x) \longrightarrow (x,f(x))\)
Linear functions can be represented by equations such as \(y=mx+b\), where \(m\) is the constant rate of change.
\(y=mx+b\)
Tables, ordered pairs, equations, and graphs are different representations of the same relationship. A point belongs on the graph when its coordinates satisfy the function rule.
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