Transformations of Parent Functions

The video tutorial covers transformations of parent functions, focusing on translations, reflections, and stretches/compressions. It explains how these transformations affect graphs and introduces the letters A, K, D, and C, which represent different types of transformations. The tutorial includes examples and practice questions to help students understand vertical and horizontal translations, vertical reflections, and vertical stretches/compressions. The importance of these transformations is highlighted, as they are revisited in later chapters on exponential and sinusoidal graphs.

Which of the following transformations involves moving a graph up or down?

• Horizontal Translation

• Vertical Translation

• Horizontal Stretch

• Vertical Reflection

If a function is translated 3 units to the right, what is the new equation form?

• f(x + 3)

• f(x) - 3

• f(x - 3)

• f(x) + 3

Which transformation does not change the shape of the graph?

• Vertical Stretch

• Horizontal Compression

• Vertical Translation

• Vertical Reflection

If a function is translated 5 units to the left and 2 units down, what is the new equation form?

• f(x - 5) + 2

• f(x - 5) - 2

• f(x + 5) - 2

• f(x + 5) + 2

What does a negative sign in front of a function indicate?

• Vertical Stretch

• Horizontal Translation

• Vertical Reflection

• Horizontal Compression

What is the parent function for a quadratic function?

• f(x) = x^2

• f(x) = x

• f(x) = |x|

• f(x) = √x

What is the effect of a vertical reflection on the graph of a function?

• The graph is mirrored over the y-axis

• The graph is moved down

• The graph is moved up

• The graph is mirrored over the x-axis

How do you identify a vertical stretch in an equation?

• The function is translated horizontally

• The coefficient of the function is greater than 1

• The coefficient of the function is between 0 and 1

• The function has a negative sign

What is the effect of a vertical compression on the shape of a graph?

• The graph is translated vertically

• The graph is reflected over the x-axis

• The graph becomes wider

• The graph becomes thinner

If a function is vertically stretched by a factor of 4 and reflected over the x-axis, what is the new equation form?

• -4f(x)

• 4f(x)

• f(-4x)

• -f(4x)