3.7.2 Transformations of Linear and Exponential Functions

Transcription

1 Name: # Honors Coordinate Algebra: Period Ms. Pierre Date:.7. Transformations of Linear and Exponential Functions Warm Up On a map, Maple Street is represented by the function f(x) = x, and Highland Street is represented by the function g(x) = x +. Graph both functions on the same set of axes.. How are the two graphs similar?. How are the two graphs different?

2 . How could you describe the geometric translation from f(x) to g(x)? It is important to understand the relationship between a function and the graph of a function. In this lesson, we will explore how a function and its graph change when a constant value is added to the function. When a constant value is added to a function, the graph undergoes a vertical shift. A vertical shift is a type of translation that moves the graph up or down depending on the value added to the function. A translation of a graph moves the graph either vertically, horizontally, or both, without changing its shape. A translation is sometimes called a slide. A translation is a specific type of transformation. A transformation moves a graph. Transformations can include reflections and rotations in addition to translations. We will also examine translations of graphs and determine how they are similar or different. Key Concepts Vertical translations can be performed on linear and exponential graphs using f(x) + k, where k is the value of the vertical shift. A vertical shift moves the graph up or down k units. If k is positive, the graph is translated up k units. If k is negative, the graph is translated down k units. Translations are one type of transformation. Given the graphs of two functions that are vertical translations of each other, the value of the vertical shift, k, can be found by finding the distance between the y-intercepts. Chant Lyrics: In the class, in the class going up, down, Signs the same, + for up, - for down K s on the street (x) Outside parentheses In the class, in the class going left, right, Signs reverse, + for left, - for right K s next to me (x) Inside parentheses

3 Example Graph the following functions on the same set of axes: f(x) = x g(x) = x + h(x) = x + q(x) = x h(x) = x + f(x) = x g(x) = x + q(x) = x 0 What is the y-intercept of f(x)? g(x)? h(x)? q(x)?

4 How could you describe the translation of h(x) from f(x)? How could you describe the translation of q(x) from f(x)? How could you describe the translation of q(x) from g(x)? Example Given f(x) = x + and the graph of f(x) below, graph g(x) = f(x) f(x) = x

5 How are f(x) and g(x) related? What are the steps you need to follow to graph g(x)?

6 Example The graphs of two functions f(x) and g(x) are shown below. Write a rule for g(x) in terms of f(x). f(x) g(x) Write a function rule for the graph of f(x). Write a function rule for the graph of g(x). How are f(x) and g(x) related? Write a function rule for g(x) in terms of f(x).

7 Guided Practice Graph the following functions of f(x) + k given the graphs of ƒ(x).. ) f(x)

8 .) f(x)

9 .) Given the graphs of f(x) and g(x) below, write a function rule for g(x) in terms of f(x). f(x) g(x)

10 4.) Given the graphs of f(x) and g(x) below, write a function rule for g(x) in terms of f(x) f(x) g(x) con

11 Independent Practice Problem-Based Task.7.: Gym Fees Paulo and Justin belong to the same gym. The graph below shows how much each man pays per month in gym fees. Both pay the same per-hour use fee, but Paulo gets an employee discount, so his monthly membership fee is different from Justin s membership fee. What is a function rule that represents Paulo s total monthly gym fees? What is a function rule that represents Justin s total monthly gym fees? What is the difference in their fees? 0 Total monthly cost ($) Justin Paulo Monthly hours of gym use

12 Homework. ) f(x) = x + and g(x) = x. If g(x) can be written as f(x) + k, what is the value of k?.) f(x) = x and g(x) = x +. If g(x) can be written as f(x) + k, what is the value of k?