Today’s Objectives: Today’s Agenda SWBAT… Sketch graphs of parent functions Define domains and ranges of common parent functions Graph functions on a calculator with a restricted domain Graph absolute value functions Name domain and range of an absolute value function 2. Notes Topic: Parent Functions Page 13 #1 – 14, 19 – 26 Handout – Absolute Value Homework:

Constant Function f(x) = c Domain  {x  x   } read as “x such that x belongs to the set of all real numbers.” Range  {y  y = c} read as “y such that y is equal to the constant value.” Features: A straight line gragh where y does not change as x changes.

Linear Function f(x) = mx + b Domain  {x  x   } Range  {y  y   } Features: A straight line graph where f(x) changes at a constant rate as x changes.

Quadratic Function f(x) = x 2 Domain  {x  x   } Range  {y  y  0} Features: Graph is shape of parabola. The graph changes direction at its one vertex.

Square Root Function f(x) = Domain  {x  x  0} Range  {y  y  0} Features: The inverse of a quadratic function where the range is restricted.

Cubic Function f(x) = x 3 Domain  {x  x   } Range  {y  y   } Features: The graph crosses the x- axis up to 3 times and has up to 2 vertices

Cube Root Function f(x) = Domain  {x  x   } Range  {y  y   } Features: The inverse of a cubic function

Power Function f(x) = Domain  {x  x   } Range  {y  y   } Features: The graph contains the origin if b is positive. In most real- world applications, the domain is nonnegative real numbers if b is positive and positive real numbers if b is negative.

Exponential Function f(x) = a  b x Domain  {x  x   } Range  {y  y > 0} Features: The graph crosses the y-axis at y = a and has the x-axis as an asymptote

Logarithmic Function f(x) = log a x Domain  {x  x > 0} Range  {y  y   } Features: The graph crosses the x- axis at 1 and has the y- axis as an asymptote.

Absolute Value Function f(x) = Domain  {x  x   } Range  {y  y  0} Features: The graph has two halves that reflect across a line of symmetry. Each half is a linear graph.

Page 13 #1 – 14, 19 – 26 Handout – Absolute Value Homework:

Polynomial Function  tionInstitute/polynomialFunctions/graphs /polynomialFunctionGraphs.html tionInstitute/polynomialFunctions/graphs /polynomialFunctionGraphs.html  *zero degree  *first Degree  *second degree  *third degree  Fourth degree