Graph Transformations and Their Effects

The video tutorial explains how to transform graphs by modifying equations. It covers changes inside and outside the brackets, affecting the x-axis and y-axis, respectively. Inside bracket changes do the opposite of what is indicated, while outside bracket changes do exactly as indicated. The tutorial also discusses the impact of negative signs, which flip the graph over the x-axis or y-axis. Examples and practice problems are provided to reinforce the concepts.

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

• A quadratic function

• A constant function

• Any function of x

• A specific linear function

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

• It shifts 3 units to the right

• It shifts 3 units to the left

• It shifts 3 units up

• It shifts 3 units down

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 flips the graph over the y-axis

• It flips the graph over the x-axis

• It shifts the graph to the left

• It shifts the graph to the right

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

• It flips over the y-axis

• It flips over the x-axis

• It shifts up

• It shifts down

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

• They double

• They become positive

• They become negative

• They remain unchanged

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

• The graph flips over the y-axis

• The graph shifts up

• The graph shifts down

• The graph flips over the x-axis

If a point on the graph is (3, -2) and the transformation is y = f(x + 5), where does the point move?

• (8, -2)

• (3, 3)

• (-2, -2)

• (3, -7)

For the transformation y = f(x) - 5, what happens to the y-coordinate of a point?

• It increases by 5

• It decreases by 5

• It remains the same

• It doubles

If a point on the graph is (3, -2) and the transformation is y = f(x) + 3, where does the point move?

• (3, 1)

• (3, -5)

• (6, -2)

• (0, -2)