Target: We will be able to identify parent functions of graphs

PARENT FUNCTIONS See handout Constant Function Inverse Linear (Identity)Inverse Squared Absolute Value Exponential Quadratic Logarithmic CubicSquare Root Greatest Integer

Constant Function f(x) = a where a = any # Even: Symmetric with y-axis

Constant Function Domain: Range: Parent Equation: f(x) = 2 Even: Symmetric with y-axis

Constant Function Parent Equation: f(x) = 2 x – intercept: y – intercept: None Even: Symmetric with y-axis

Constant Function Graph Description: Horizontal Line Table: xy Parent Equation: f(x) = 2

Linear Function (Identity) f(x) = x Odd: Symmetric with origin

Linear Function (Identity) Domain: Range: Parent Equation: f(x) = x Odd: Symmetric with origin

Linear Function (Identity) Parent Equation: f(x) = x x – intercept: y – intercept:

Linear Function (Identity) Parent Equation: f(x) = x Table: xy Graph Description: Diagonal Line Odd: Symmetric with origin

Absolute Value Function f(x) = │ x │ Even: Symmetric with y-axis

Absolute Value Function Domain: Range: Parent Equation: f(x) = │ x │

Absolute Value Function Parent Equation: f(x) = │x │ x – intercept: y – intercept:

Absolute Value Function Table: xy Parent Equation: Graph Description: “V” - shaped f(x) = │ x │

f(x) = x 2 Quadratic Function Even: Symmetric with y-axis

f(x) = x 2 Quadratic Function Domain: Range: Parent Equation:

Quadratic Function Parent Equation: x – intercept: y – intercept: f(x) = x 2

Quadratic Function Table: xy Parent Equation: Graph Description: “U” - shaped

Cubic Function f(x) = x 3 Odd: Symmetric with origin

Cubic Function f(x) = x 3 Domain: Range: Parent Equation: Odd: Symmetric with origin

Cubic Function f(x) = x 3 Parent Equation: x – intercept: y – intercept:

Cubic Function f(x) = x 3 Parent Equation: Table: xy

f(x) = x Square Root Function Neither even nor odd

f(x) = x Square Root Function Domain: Range: Parent Equation: Neither even nor odd

f(x) = x Square Root Function Parent Equation: x – intercept: y – intercept:

f(x) = x Square Root Function Parent Equation: Table: xy Graph Description: Horizontal ½ of a Parabola

f(x) = 1 x Inverse Function or Rational Function (Reciprocal of x) Odd: Symmetric with origin

f(x) = 1 x Inverse Function or Rational Function (Reciprocal of x) Parent Equation: Domain: Range:

f(x) = 1 x Inverse Function or Rational Function (Reciprocal of x) Parent Equation: x – intercept: y – intercept:

Inverse Function or Rational Function (Reciprocal of x) Table: xy Error f(x) = 1 x Parent Equation: Odd: Symmetric with origin

Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2

Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2 Parent Equation: Domain: Range:

Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2 x – intercept: y – intercept: Parent Equation:

Inverse Squared Function (Reciprocal of x 2 ) f(x) = 1 x 2x 2 Parent Equation: Table: xy Error

Exponential Function b = base and x = exponent Neither even nor odd

f(x) = 2 x Exponential Function Domain: Range: Parent Equation: Neither even nor odd

f(x) = 2 x Exponential Function x – intercept: y – intercept: Parent Equation:

f(x) = 2 x Exponential Function Table: xy Parent Equation: Graph Description: Backwards “L” Curves

f(x) = log x Logarithmic Function

f(x) = log x Logarithmic Function Range: Parent Equation: Domain:

f(x) = log x Logarithmic Function x – intercept: y – intercept: Parent Equation: Neither even nor odd

Logarithmic Function Table: xy -2Error Error Parent Equation: f(x) = log x

Step Function (Greatest Integer) f(x) = [x] Neither even nor odd

Step Function (Greatest Integer) f(x) = [x] Domain: Range: Parent Equation:

Step Function (Greatest Integer) f(x) = [x] Parent Equation: x – intercept: y – intercept:

Step Function (Greatest Integer) f(x) = [x] Parent Equation: Graph Description: Stair Steps Table: xy

HW 1.5: Use a graphing calculator, or online graphing utility to graph #19-41 odd, p 71