Identity function | f(x) = x |

Square function | h(x) = x^{2} |

Cube function | m(x) = x^{3} |

Square root function | n(x) = √x |

Cube root function | p(x) = ∛x |

Absolute value function | g(x) = |x| |

Adding a constant *k* to the function *f(x)*:

y = f(x) + k

- Shifts the graph of
*y = f(x)*up*k*units if*k > 0*. - Shifts the graph of
*y = f(x)*down*k*units if*k < 0*.

Drag the slider to add or subtract a constant *k* to the function.

Adding a constant *h* to the value of *x* in the function *f(x)*:

y = f(x + h)

- Shifts the graph of
*y = f(x)*left*h*units if*h > 0*. - Shifts the graph of
*y = f(x)*right*|h|*units if*h < 0*.

Drag the slider to shift the function a constant *h* left or right.

Multiplying the function *f(x)* by -1:

y = -f(x)

This reflects the graph of *y = f(x)* in the *x* axis.

Multiplying the function *f(x)* by a constant *A*:

y = Af(x)

- Stretches the graph of
*y = f(x)*vertically by a factor of*A*if*A > 1*. - Shrinks the graph of
*y = f(x)*vertically by a factor of*A*if*0 < A < 1*.

Drag the slider to multiply the function by a constant *A*.