Transformations of Functions and Graphs

The video tutorial covers graph transformations, focusing on translations along the y-axis and x-axis. It explains how adding or subtracting a value outside the function affects the y-coordinates, moving the graph up or down. Similarly, changes inside the function affect the x-coordinates, shifting the graph left or right. The tutorial includes examples to illustrate these concepts, emphasizing the importance of correctly labeling new coordinate points.

What is the primary effect of a translation on a graph?

• It reflects the graph over the x-axis.

• It rotates the graph around the origin.

• It moves every point on the graph a fixed distance in the same direction.

• It changes the shape of the graph.

How does a positive value of 'e' outside the bracket affect the graph of f(x)?

• It moves the graph to the left.

• It moves the graph to the right.

• It moves the graph down.

• It moves the graph up.

If f(x) is transformed to f(x) + 5, what happens to the graph?

• It moves 5 units up.

• It moves 5 units to the right.

• It moves 5 units to the left.

• It moves 5 units down.

In the example of f(x) - 3, what is the effect on the y-coordinates?

• Add 3 to each y-coordinate.

• Subtract 3 from each y-coordinate.

• Multiply each y-coordinate by 3.

• Divide each y-coordinate by 3.

What is the effect of f(x) + 1 on the graph?

• The graph moves 1 unit down.

• The graph moves 1 unit to the left.

• The graph moves 1 unit to the right.

• The graph moves 1 unit up.

What is the effect of f(x) - 2 on the graph?

• The graph moves 2 units up.

• The graph moves 2 units to the right.

• The graph moves 2 units to the left.

• The graph moves 2 units down.

What happens to the graph of f(x) when transformed to f(x + e) with a positive 'e'?

• The graph moves left.

• The graph moves right.

• The graph moves up.

• The graph moves down.

If f(x) is transformed to f(x - 2), what is the effect on the graph?

• It moves 2 units to the right.

• It moves 2 units to the left.

• It moves 2 units down.

• It moves 2 units up.

What is the effect of a negative 'e' inside the bracket on the graph of f(x)?

• The graph moves left.

• The graph moves right.

• The graph moves up.

• The graph moves down.

If f(x) is transformed to f(x + 4), what is the effect on the graph?

• It moves 4 units down.

• It moves 4 units up.

• It moves 4 units to the right.

• It moves 4 units to the left.