Graph Transformations and Their Effects

This video tutorial covers the topic of transforming graphs, focusing on how changes inside and outside the brackets of a function affect the graph's position. Inside bracket changes affect the x-axis and do the opposite of what is indicated, while outside bracket changes affect the y-axis and do exactly what is indicated. The video also explains the impact of negative signs on transformations, flipping the graph over the x-axis or y-axis. Several examples are provided to illustrate these concepts, including how to determine new coordinates after transformations.

What does the function y = f(x) represent in the context of graph transformations?

• Any function of x

• A constant function

• A specific quadratic function

• A linear function

If the transformation is y = f(x - 3), what happens to the graph?

• It shifts 3 units down

• It shifts 3 units up

• It shifts 3 units to the left

• It shifts 3 units to the right

How does a change outside the bracket, such as y = f(x) + 2, affect the graph?

• It shifts the graph 2 units to the left

• It shifts the graph 2 units to the right

• It shifts the graph 2 units up

• It shifts the graph 2 units down

What is the effect of a negative sign outside the function, as in y = -f(x)?

• It shifts the graph downwards

• It shifts the graph upwards

• It flips the graph over the x-axis

• It flips the graph over the y-axis

In the transformation y = f(-x), what happens to the graph?

• It flips over the x-axis

• It flips over the y-axis

• It shifts to the left

• It shifts to the right

If a graph has a minimum point at (3, -2) and is transformed by y = f(x + 5), where does the minimum point move?

• To (8, -2)

• To (3, -7)

• To (-2, -2)

• To (3, 3)

What happens to the y-values when the transformation is y = f(x) - 5?

• They decrease by 5

• They remain the same

• They are multiplied by 5

• They increase by 5

In the transformation y = f(x) + 3, what happens to the graph?

• It shifts 3 units up

• It shifts 3 units to the left

• It shifts 3 units down

• It shifts 3 units to the right

If the transformation is y = f(-x), what happens to the x-values?

• Positive x-values become negative

• Negative x-values become positive

• Both a and b

• Neither a nor b

What is the result of applying y = -f(x) to a graph?

• The graph is flipped over the x-axis

• The graph is flipped over the y-axis

• The graph is shifted downwards

• The graph is shifted upwards