Exploring Linear Transformations

The video tutorial covers linear transformations, focusing on how lines change from their parent function y = x. It explains the concepts of slope and y-intercept, and how transformations can shift lines vertically and horizontally. The tutorial also discusses how multiplying factors can alter the slope, making it steeper or less steep. Examples are provided to illustrate these transformations.

What is the parent function in linear transformations?

• y = x^2

• y = x

• y = 2x + 3

• y = 1/x

What happens to the graph of a function when a value is added outside the function?

• It shifts up

• It shifts to the right

• It shifts down

• It shifts to the left

If a value is subtracted outside the function, how does the graph shift?

• It shifts to the left

• It shifts down

• It shifts up

• It shifts to the right

How does the graph shift when a value is added inside the function?

• It shifts down

• It shifts to the left

• It shifts to the right

• It shifts up

What is the effect of subtracting a value inside the function?

• The graph shifts up

• The graph shifts down

• The graph shifts to the left

• The graph shifts to the right

In the example g(x) = f(x) + 6, how does the graph shift?

• Left 6 units

• Down 6 units

• Up 6 units

• Right 6 units

For the function h(x) = f(x) - 8, what is the shift direction?

• Right 8 units

• Left 8 units

• Down 8 units

• Up 8 units

What happens to the slope if a factor greater than 1 is multiplied to the function?

• The slope becomes less steep

• The slope becomes steeper

• The slope remains the same

• The slope becomes zero

If a factor between 0 and 1 is multiplied to the function, how does the slope change?

• The slope becomes less steep

• The slope becomes zero

• The slope becomes steeper

• The slope remains the same

What is the effect of multiplying the input value by a factor?

• It changes the y-intercept

• It changes the slope

• It shifts the graph vertically

• It shifts the graph horizontally