Understanding Vertical Shifts in Functions

The video tutorial explains how to translate the graph of the function f(x) = 3x - 4 upwards by 2 units using a K value. The K value is the number by which the graph is translated vertically. The tutorial demonstrates that adding 2 to the function, f(x) + 2, shifts the graph up by 2 units. It visually illustrates this by moving each point on the graph up by 2 units and connecting them to form the new graph. The tutorial emphasizes that the K value is positive, indicating an upward shift, and concludes by reiterating the process of graph translation using the K value.

What does the K value represent in the function F(x) + K?

• The x-intercept of the graph

• The vertical shift of the graph

• The horizontal shift of the graph

• The slope of the graph

If you want to move the graph of F(x) = 3x - 4 up by 3 units, what should be the value of K?

• 0

• 3

• 4

• -3

How does the graph change when you apply a positive K value?

• It shifts to the left

• It moves upwards

• It shifts to the right

• It moves downwards

What happens to each point on the graph when it is translated upwards by a K value?

• Each point is moved down

• Each point is moved up

• Each point is moved to the right

• Each point is moved to the left

Why doesn't the graph move horizontally when a positive K value is applied?

• Because K is negative

• Because K only affects vertical movement

• Because K affects both vertical and horizontal movement

• Because K is a constant

What is the effect of a negative K value on the graph?

• It moves the graph to the right

• It moves the graph upwards

• It moves the graph to the left

• It moves the graph downwards