Transformations of Linear Function Graphs

This video tutorial covers the concept of transformations in functions, including translations, reflections, and dilations. It begins with an introduction to parent functions and explains how other functions are transformations of these parent functions. The tutorial then delves into specific types of transformations: translations, which slide the graph; reflections, which flip the graph over an axis; and dilations, which stretch or shrink the graph. Each transformation is explained with examples and graphing exercises to help students understand the changes in function notation and graph behavior.

What is the most basic function in a family of functions called?

• Child function

• Cousin function

• Sibling function

• Parent function

What does a transformation change in a function?

• Only the size

• Size, shape, position, or orientation

• Only the position

• Only the shape

What is a translation in the context of function transformations?

• A flip of the function over a line

• A slide of the function across the grid

• A change in the slope of the function

• A stretch or shrink of the function

In a translation, what happens to the function when you add a constant to the y-values?

• The function reflects over the x-axis

• The function shifts vertically

• The function shifts horizontally

• The function reflects over the y-axis

What is a reflection in the context of function transformations?

• A slide of the function across the grid

• A flip of the function over a line of symmetry

• A change in the slope of the function

• A stretch or shrink of the function

When a function is reflected over the x-axis, which values change?

• Neither x nor y values

• Both x and y values

• The y-values

• The x-values

What is a dilation in the context of function transformations?

• A change in the slope of the function

• A stretch or shrink of the function

• A flip of the function over a line of symmetry

• A slide of the function across the grid

What happens to the graph of a function when it undergoes a horizontal stretch?

• The graph becomes steeper

• The graph shifts vertically

• The graph reflects over the y-axis

• The graph becomes flatter

What is the effect of multiplying the y-values of a function by a constant greater than 1?

• The graph reflects over the x-axis

• The graph becomes flatter

• The graph becomes steeper

• The graph shifts horizontally

What is the official mathematical term for making a graph steeper by multiplying the y-values?

• Horizontal shrink

• Vertical stretch

• Vertical shrink

• Horizontal stretch