Parent Functions (Identify Different Ways)

Linear Function

A function defined by the equation $y = x$, represented visually as a straight line passing through the origin.

Quadratic (Square) Function

A function defined by the equation $y = x^2$, which creates a U-shaped graph called a parabola.

Square ROOT Function

A function defined by the equation $y = √(x)$, representing a curve that starts at $(0,0)$ and extends into the first quadrant.

Cubic Function

A function defined by the equation $y = x^3$, characterized by a vertical S-curve passing through the origin.

Cube ROOT Function

A function defined by the equation $y = \sqrt[3]{x}$, characterized by a horizontal S-curve extending across all four quadrants.

Rational - linear Function

A function defined by the equation $y = \frac{1}{x}$, featuring two hyperbolas in opposite quadrants separated by vertical and horizontal asymptotes.

Rational - quadratic Function

A function defined by the equation $y = \frac{1}{x^2}$, consisting of two symmetrical curves above the x-axis approaching a vertical asymptote at $x = 0$.

EXPONENTial Function

A function defined by the equation $y = 2^x$, featuring rapid upward growth for positive values of $x$ and approaching a horizontal asymptote along the negative x-axis.

Logarithmic Function

A function defined by the equation $y = \log(x)$, featuring a curve with a vertical asymptote along the negative y-axis that gradually flattens out as $x$ increases.

Absolute Value Function

A function defined by the equation $y = |x|$, forming a V-shaped graph with a vertex at the origin.

$$y = x$$

Linear Function

$$y = x^2$$

Quadratic (Square) Function

$$y = √(x)$$

Square ROOT Function

$$y = x^3$$

Cubic Function

$$y = \sqrt[3]{x}$$

Cube ROOT Function

$$y = \frac{1}{x}$$

Rational - linear Function

$$y = \frac{1}{x^2}$$

Rational - quadratic Function

$$y = 2^x$$

EXPONENTial Function

$$y = \log(x)$$

Logarithmic Function

$$y = |x|$$

Absolute Value Function

Linear Function

$$y = x$$

Quadratic (Square) Function

$$y = x^2$$

Square ROOT Function

$$y = √(x)$$

Cubic Function

$$y = x^3$$

Cube ROOT Function

$$y = \sqrt[3]{x}$$

Rational - linear Function

$$y = \frac{1}{x}$$

Rational - quadratic Function

$$y = \frac{1}{x^2}$$

EXPONENTial Function

$$y = 2^x$$

Logarithmic Function

$$y = \log(x)$$

Absolute Value Function

$$y = |x|$$