Understanding Graph Transformations

The video tutorial explains the effect of adding a constant to a function f(x), specifically focusing on how adding a positive constant shifts the graph of the function upward. The instructor uses a quadratic function as an example, demonstrating that each point on the graph moves up by the constant value. The tutorial concludes by emphasizing that the graph shifts up, not down, and not sideways.

What is the initial step in understanding the effect of adding a constant to a function's graph?

• Drawing the original graph

• Identifying the type of function

• Calculating the derivative

• Finding the x-intercepts

What happens to the graph of a function when a positive constant is added?

• It shifts downwards

• It shifts upwards

• It shifts to the left

• It shifts to the right

How does adding a positive constant affect each point on the graph?

• Each point moves up

• Each point moves down

• Each point moves left

• Each point moves right

What is the result of connecting the dots after shifting each point up by one unit?

• A graph with a different slope

• A new graph with a different shape

• The same graph shifted down

• The same graph shifted up

What is the effect of adding a negative constant to a function's graph?

• The graph shifts right

• The graph shifts left

• The graph shifts down

• The graph shifts up

Which of the following is NOT a result of adding a constant to a function's graph?

• Shifting the graph left or right

• Shifting the graph down

• Shifting the graph up

• Changing the graph's shape

What is the primary focus of the video tutorial?

• Solving quadratic equations

• Understanding graph transformations

• Finding the roots of a function

• Calculating the area under a curve

What is the key takeaway from the video regarding graph transformations?

• Adding a constant changes the graph's slope

• Adding a constant shifts the graph vertically

• Adding a constant changes the graph's curvature

• Adding a constant affects the graph's x-intercepts