 Show Section 1.1 Parent Functions and Transformations 3 Parent Functions and Transformations 1.1 Essential QuestionEssential Question What are the characteristics of some of the basic parent functions? Identifying Basic Parent Functions Work with a partner. Graphs of eight basic parent functions are shown below. Classify each function as constant, linear, absolute value, quadratic, square root, cubic, reciprocal, or exponential. Justify your reasoning. a. 6 −4 −6 4 b. 6 −4 −6 4 c. 6 −4 −6 4 d. 6 −4 −6 4 e. 6 −4 −6 4 f. 6 −4 −6 4 g. 6 −4 −6 4 h. 6 −4 −6 4 Communicate Your AnswerCommunicate Your Answer 2. What are the characteristics of some of the basic parent functions? 3. Write an equation for each function whose graph is shown in Exploration 1. Then use a graphing calculator to verify that your equations are correct. JUSTIFYING CONCLUSIONS To be profi cient in math, you need to justify your conclusions and communicate them clearly to others. About this unitIn Algebra 1, students reasoned about graphs of absolute value and quadratic functions by thinking of them as transformations of the parent functions |x| and x². In this unit, we extend this idea to include transformations of any function whatsoever. This fascinating concept allows us to graph many other types of functions, like square/cube root, exponential and logarithmic functions. How do you Transformations from the parent function?The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.
What are the Transformations in Algebra 2?A transformation is an alteration to a parent function's graph. There are three types of transformations: translations, reflections, and dilations.
What is a parent function in Algebra 2?A parent function is the simplest function of a family of functions. For the family of quadratic functions, y = ax2 + bx + c, the simplest function. of this form is y = x2. The "Parent" Graph: The simplest parabola is y = x2, whose graph is shown at the right.
What is the parent function of a line?For linear functions, the parent function is y = x or f(x) = x.
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Algebra 2 parent functions and transformations worksheet
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