Exploring Linear Function Transformations

This video tutorial covers graphing linear functions, starting with the parent function y = x. It explains how to graph transformations such as vertical shifts, changes in steepness, and reflections. The tutorial includes examples like y = x + 2, y = x - 3, y = 2x, y = 0.5x, y = -x, y = 2x + 3, and y = -0.5x - 1, demonstrating how each transformation affects the graph.

What is the parent function of a linear function?

• y = x

• y = x^2

• y = 2x

• y = x + 1

If the parent function y = x is shifted up by 2 units, what is the new equation?

• y = 2x

• y = x/2

• y = x + 2

• y = x - 2

What happens to the graph of y = x when it is transformed to y = x - 3?

• It becomes steeper

• It shifts down by 3 units

• It becomes less steep

• It shifts up by 3 units

How does the graph of y = 2x compare to the parent function y = x?

• It becomes steeper

• It shifts down by 2 units

• It becomes less steep

• It shifts up by 2 units

What is the effect on the graph when the equation is y = 1/2x?

• It becomes less steep

• It becomes steeper

• It shifts down by 1/2 unit

• It shifts up by 1/2 unit

What transformation occurs when the equation changes from y = x to y = -x?

• It reflects across the x-axis

• It shifts down

• It reflects across the y-axis

• It shifts up

In the equation y = 2x + 3, what does the '+3' represent?

• A shift up by 3 units

• A reflection across the x-axis

• A shift down by 3 units

• A reflection across the y-axis

What is the combined effect of the transformations in the equation y = 2x + 3?

• Shift down by 2 units and less steep

• Shift up by 3 units and more steep

• Shift down by 3 units and more steep

• Shift up by 2 units and less steep

What is the effect of the transformation in the equation y = -1/2x - 1?

• Shift down by 2 units and more steep

• Shift up by 1 unit and more steep

• Shift down by 1 unit and less steep

• Shift up by 2 units and less steep

If the equation is y = -1/2x - 1, what is the y-value when x = 2?

• 0

• -2

• 1

• -1