Parent Functions

To solve complex equations

To understand the behavior of different functions

To memorize mathematical formulas

To perform arithmetic operations

f(x) = a(x-h)^2 + k

f(x) = ax^2 + bx + c

f(x) = a(x-h)^3 + k

f(x) = a√(x-h) + k

The domain of a square root function is [0, ∞), while a quadratic function is (-∞, ∞).

The domain of a square root function is (-∞, ∞), while a quadratic function is [0, ∞).

Both have the same domain.

The domain of a square root function is (-∞, 0], while a quadratic function is (-∞, ∞).

Both approach infinity as x approaches infinity.

Cubic functions approach infinity, while cube root functions approach zero.

Cubic functions approach zero, while cube root functions approach infinity.

Both approach zero as x approaches infinity.

Reflect over the x-axis, vertical stretch by 3, translate down 1

Reflect over the y-axis, vertical compression by 3, translate up 1

Reflect over the x-axis, vertical compression by 3, translate down 1

Reflect over the y-axis, vertical stretch by 3, translate up 1

Expand horizontally by a factor of 2, translate right 1 unit, translate up 3 units

Compress horizontally by a factor of 2, translate left 1 unit, translate down 3 units

Expand horizontally by a factor of 2, translate left 1 unit, translate up 3 units

Compress horizontally by a factor of 2, translate right 1 unit, translate down 3 units

(-∞, ∞)

[0, ∞)

(-∞, 0]

[0, 0]