Parent Quadratic Function: \(y=x^2\)

Domain: \(\{x ~ | ~ x \in \mathbb{R}\}\)

Range: \(\{y ~ | ~ y \geq 0, y \in \mathbb{R}\}\)

Function: \(y=-2(x-1)^2+3\)

Domain: \(\{x ~ | ~ x \in \mathbb{R}\}\)

Range: \(\{y ~ | ~ y \leq 3, y \in \mathbb{R}\}\)

Parent Cubic Function: \(y=x^3\)

Domain: \(\{x ~ | ~ x \in \mathbb{R}\}\)

Range: \(\{y ~ | ~ y \in \mathbb{R}\}\)

Parent Quartic Functions: \(y=x^4\)

Domain: \(\{x ~ | ~ x \in \mathbb{R}\}\)

Range: \(\{y ~ | ~ y \geq 0, y \in \mathbb{R}\}\)

Transformations on a function \(y=f(x)\) can be identified when the function is in the form

Cubic \(f(x)=x^3\)

Quartic \(f(x)=x^4\)

Let's review the role of the parameters \(a\), \(b\), \(h\), and \(k\) in transforming these functions.