Exploring Linear Transformations in Algebra

The video tutorial covers the basics of linear functions, focusing on parent functions and their transformations. It explains how to graph linear functions using a calculator and delves into the concepts of horizontal and vertical translations. The tutorial provides examples and exercises to help students understand how these translations affect the graph of a function.

What is the parent linear function?

• f(x) = x^2

• f(x) = x

• f(x) = 2x

• f(x) = x + 1

Which of the following is true about the parent linear function?

• It is a quadratic function.

• It is a constant function.

• It is a linear function.

• It is an exponential function.

How do you graph the parent linear function using a calculator?

• Enter y = x^2 and press Enter.

• Enter y = 2x and press Enter.

• Enter y = x + 1 and press Enter.

• Enter y = x and press Enter.

What is the slope of the parent linear function f(x) = x?

• 0

• 1

• 2

• Undefined

What does a horizontal translation of f(x) = x + 3 represent?

• Shift down 3 units

• Shift right 3 units

• Shift left 3 units

• Shift up 3 units

If f(x) = x and g(x) = f(x - 4), what is the translation?

• Shift down 4 units

• Shift up 4 units

• Shift right 4 units

• Shift left 4 units

What does a vertical translation of f(x) = x + 2 represent?

• Shift up 2 units

• Shift right 2 units

• Shift left 2 units

• Shift down 2 units

If f(x) = x and h(x) = f(x) - 5, what is the translation?

• Shift up 5 units

• Shift right 5 units

• Shift left 5 units

• Shift down 5 units

Which of the following describes a horizontal translation of f(x) = x to g(x) = f(x + 4)?

• Shift up 4 units

• Shift left 4 units

• Shift down 4 units

• Shift right 4 units

If f(x) = x and h(x) = f(x) + 3, what is the translation?

• Shift left 3 units

• Shift right 3 units

• Shift up 3 units

• Shift down 3 units