Interactive Function Graphs

Search, hover, and open classroom-ready graphs. Four core functions are enlarged for quick teaching, while the rest stay compact for fast browsing.

Featured Classroom Graphs

Quadratic $y = x^{2}$

A quadratic function is a degree-two polynomial. Its graph is a parabola, useful for discussing symmetry, turning points, and rates of change.

Hover over the graph Sine $y = \sin (x)$

The sine function is periodic and comes from trigonometry. It is a natural model for waves, rotations, and repeating classroom phenomena.

Hover over the graph Exponential $y = 2^{x}$

An exponential function has the input in the exponent. It helps show repeated growth, decay, and how equal x-steps can multiply y-values.

Hover over the graph Transform Quadratic $y = a {(x - h)}^{2} + k$

Vertex form makes transformations visible: a changes opening and stretch, while h and k move the parabola horizontally and vertically.

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More Function Graphs

Linear $y = x$

A linear function graphs as a straight line and changes by a constant amount for each equal step in x.

Hover over the graph Absolute Value $y = | x |$

Absolute value measures distance from zero. Its graph forms a sharp V, making reflection and piecewise behavior easy to see.

Hover over the graph Reciprocal $y = \frac{1}{x}$

The reciprocal function is undefined at zero and approaches both axes, giving a clear introduction to asymptotes.

Hover over the graph Constant $y = 2$

A constant function keeps the same output for every input. Its graph is a horizontal line with zero rate of change.

Hover over the graph Cubic $y = x^{3}$

A cubic function is a degree-three polynomial. The parent graph passes through the origin and shows odd symmetry.

Hover over the graph Square Root $y = \sqrt{x}$

The square root function starts at zero in the real plane and grows slowly, making domain restrictions visible.

Hover over the graph Cube Root $y = \sqrt[3]{x}$

The cube root function accepts positive and negative inputs and is the inverse pattern of the cubic parent function.

Hover over the graph Logarithmic $y = \ln (x)$

A logarithmic function is the inverse of exponential growth. It is defined for positive inputs and grows more slowly over time.

Hover over the graph Cosine $y = \cos (x)$

Cosine is another periodic trigonometric function. Its graph matches sine in shape but starts at a maximum when x is zero.

Hover over the graph Tangent $y = \tan (x)$

Tangent is periodic and has repeating vertical asymptotes, which makes discontinuities and undefined values visible.

Hover over the graph Negative Linear $y = - x$

This decreasing line has slope -1, giving a simple contrast with the parent linear function y = x.

Hover over the graph Inverse Square $y = \frac{1}{x^{2}}$

The inverse square function is always positive except where undefined, and it rises sharply near x = 0.

Hover over the graph Step Function $y = ⌊ x ⌋$

The floor function returns the greatest integer less than or equal to x, producing a staircase graph.

Hover over the graph Ceiling Function $y = ⌈ x ⌉$

The ceiling function returns the least integer greater than or equal to x, forming a shifted staircase pattern.

Hover over the graph Semicircle $y = \sqrt{9 - x^{2}}$

This graph is the upper half of a circle with radius 3, useful for connecting functions with geometric constraints.

Hover over the graph Gaussian $y = e^{- x^{2}}$

A Gaussian has a bell-shaped curve centered at its peak, often used to introduce distribution-like shapes and rapid decay.

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How teachers can use this graphing tool

Use the enlarged cards for whole-class comparison, then search for a specific parent function when a lesson moves to a new family of graphs.

Classroom activities

Search for related functions, such as sine, cosine, and tangent, and compare their shapes.
Ask students to predict whether a function will be continuous before opening its detail page.
Use the descriptions as quick prompts before discussing the graph formally.

Common misconceptions

Students often remember formulas without connecting them to shape. Pairing each graph with a short explanation keeps the algebraic and visual meanings together.