 ## Tutoring on Determining Transformations of Functions

Learning Objectives:

#### Understand to Determine the Transformations of Functions.

Determining Transformations of Functions

Vertical Stretch and Vertical Compression: To transform the function f(x) to a(b(x+c)) +d. Let's first talk about the value of "a." y = a f(x), for a ˃ 1, we'll stretch the graph of f(x) vertically by a factor of "a."  y =a f(x), for 0 ˂a ˂ 1, we'll compress the graph of f(x) vertically by a factor of "a." One way to find coordinates of a transformed function in this form would be to find points on the parent function, keep the x coordinates the same, but multiply the y coordinates by "a" to find the y coordinates of the transformed function.

Horizontal Stretch and Horizontal Compression: To transform the function f(x) to a (b(x+c)) +d. Let's first talk about the value of "b." y = f(b x), for b ˃ 1, we'll compress the graph of f(x) horizontally by a factor of "b." y = f(b x),  for 0 ˂b ˂ 1, we'll stretch the graph of f(x) horizontally . Reflections over the x-axis and y-axis:  To do the reflection of the function f(x) to a(b(x+c)) +d. y= -f(x)  for a ˂0 reflects f(x) about x-axis. y= f(-x)  for b ˂0 reflects f(x) about y-axis.

Hook Questions:

1.    What is meant by vertical stretch?

2.    What is horizontal compression?

3.    What is meant by reflection of a function about x-axis?

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