Parent Functions

I told you not to go out tonight y=3x-2! You are grounded for 2 weeks! And no computer either!

What is a parent function

• A parent function is the most basic form of a function. It has the same basic properties as others like it but is isn’t moved any direction neither is a stretched or skewed any way

Why do we care?

• Parent functions allow us to quickly tell certain traits of their “children”.

• My parent both have brown eyes and I have brown eyes. Most people could guess the color of my eyes by meeting my parents

The constant

• y = c; f(x) = c• c is some constant number such as 3, 27, 18

million, π or e.

• Domain: all reals; int: (-∞, ∞); ineq: x• Range: c; int: [c,c]; ineq: y = c

Linear (Identity)

• y = x; f(x) = x• Domain: all reals; int: (-∞, ∞); ineq: x• Range: all reals; int: (-∞, ∞); ineq: y

Quadratic

• y = x²; f(x) = x² • Domain: all reals; int: (-∞, ∞); ineq: x• Range: int: [0, ∞); ineq: y ≥ 0

Absolute Value

• y = |x|; f(x) = |x|• Domain: all reals; int: (-∞, ∞); ineq: x• Range: int: [0, ∞); ineq: y ≥ 0

Exponential

• y = ex; f(x) = ex

• Domain: all reals; int: (-∞, ∞); ineq: x• Range: int: [0, ∞); ineq: y ≥ 0

Example

• y = x• Domain: {0, 1, 2}

• Range: _______________________________

• Parent Function:________________________

Example

• f(x) = ½• Domain: {0, 2, 4}

• Range: _______________________________

• Parent Function:________________________

Example

• y = x2

• Domain: {1, 0, 1}

• Range: _______________________________

• Parent Function:________________________

Example

• y = -¾x + 2• Domain: {0, 4, 8}

• Range: _______________________________

• Parent Function:________________________