Cubic, Square Root, and Reciprocal Functions 1. The graph of the cubic function f (x) = x3 has the following characteristics. • Domain: the set of all real numbers. • Range: the set of all real numbers. • The function is odd. • The graph has an intercept at (0, 0). Now that we are comfortable with these eight parent functions, lets play with them a little be by changing a thing or two in their equations and seeing how it affects the graph: Let’s transform them. Follow these easy steps to easily sketch transformations of any parent function. 1. Identify the parent or original function. 2. KEY to Chart of Parent Functions with their Graphs, Tables, and Equations Name of Parent Function Graph of Function Table of Values Equation of Parent Function Special Features or.

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graphs of parent functions pdf

Graphing Transformations of Parent Functions, time: 19:02

Parent Functions “Cheat Sheet” 20 September Function Name Parent Function Graph Characteristics Algebra Constant B: T ; L? Domain: (∞, ∞) Range: [c, c] Inverse Function: Undefined (asymptote) Restrictions: c is a real number Odd/Even: Even General Form: # U E $ L0 Linear or Identity. KEY to Chart of Parent Functions with their Graphs, Tables, and Equations Name of Parent Function Graph of Function Table of Values Equation of Parent Function Special Features or. Transformations and Parent Functions The "stretch" (or "shrink"): a This transformation expands (or contracts) the parent function up and down (along the y-axis). If a > 1, the ftnction's rate of change increased. If 0. PARENT FUNCTIONS f(x)= a f(x)= x f(x)= x f(x)==int()x []x Constant Linear Absolute Value Greatest Integer f(x)= x2 f(x)= x3 f(x)= x f(x)= 3 x Quadratic Cubic Square Root Cube Root f(x)= ax f(x)= loga x 1 f(x) x = ()() ()() x12 x2 f(x) x1x2 +− = +− Exponential Logarithmic Reciprocal Rational f(x)= sinx f(x)= cosx f(x) = tanx Trigonometric Functions. Every trigonometric function has a period. The periods of the parent functions are as follows: for sine, cosine, secant and cosecant, period L 2π; for tangent and cotangent, period L π. For the general function, B:T;, defined above, period L n _ p c l r r c p g m b F. Cubic, Square Root, and Reciprocal Functions 1. The graph of the cubic function f (x) = x3 has the following characteristics. • Domain: the set of all real numbers. • Range: the set of all real numbers. • The function is odd. • The graph has an intercept at (0, 0). The purpose of this lesson is to introduce students to some of the Parent Functions, and the vocabulary used to explain graphs. After reviewing the Warm Up, I hand students a list of Graphing Vocabulary, and a Graphic Organizer for students to take notes on the Parent timmerdraget.org: Rhonda Leichliter. function shown, where g(x) is the vertical distance in feet of the ball from the ground and x is the horizontal distance in feet such that x = 0 corresponds to the initial point. a. Describe the transformation(s) of the parent function f(x) = x2 used to graph . Now that we are comfortable with these eight parent functions, lets play with them a little be by changing a thing or two in their equations and seeing how it affects the graph: Let’s transform them. Follow these easy steps to easily sketch transformations of any parent function. 1. Identify the parent or original function. 2. For problem 1- 6, please give the name of the parent function and describe the transformation represented. You may use your graphing calculator to compare & sketch. For problems 10 – 14, given the parent function and a description of the transformation, write the equation of the transformed function.PARENT FUNCTIONS f(x) a. = f(x) x. = f(x) x. = () [ ] f(x) int x x. = = Constant. Linear. Absolute Value. Greatest Integer. 2 f(x) x. = 3 f(x) x. = f(x) x. = 3 f(x) x.. Harold's. Parent Functions. “Cheat Sheet”. 20 September Function. Name. Parent. Function. Graph. Characteristics. Algebra. Constant. Domain: (∞, ∞). KEY to Chart of Parent Functions with their Graphs, Tables, and Equations. Name of Parent. Function. Graph of Function. Table of Values. Equation of Parent. Common Parent Functions. Tutoring and Learning Centre, George Brown College timmerdraget.org Linear Function: f(x) = x. Domain: All real . What type of function is given on the right? b. What is the equation of the function ? 4. a. Describe what happened to the parent function for the graph at the right. Functions. Chapter 3. BIG IDEA Knowledge of the features and graphs of parent functions helps in analyzing more complex functions. Parent Functions. Below are graphs of parents functions used in Algebra 2. It is important that you are able to recognize a function by its equation and its graph. GRAPHS OF PARENT FUNCTIONS. Linear Function. Absolute Value Function. Square Root Function. *. AL f(x) = inx + b f(x) = |x| = 1, x2 0 f(x) = x. (-1, x < 0. 2. PART I: Parent Functions and FAMILIES. What is a Parent Function: Confirm your answer by plotting the points and observing the graph. 1. 2. 3. 4. x -2 0 1. -

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