Understanding Vertical Stretching and Shrinking of Graphs

What happens to the graph of f(x) = x^2 when it is transformed to g(x) = 3x^2?

• It becomes wider.

• It becomes narrower.

• It shifts upwards.

• It shifts downwards.

In the transformation h(x) = 1/3 * x^2, what is the effect on the graph of f(x) = x^2?

• The graph shifts to the right.

• The graph shifts to the left.

• The graph becomes wider.

• The graph becomes narrower.

What determines whether a graph undergoes a vertical stretch or shrink?

• The degree of the polynomial.

• The absolute value of the constant multiplier.

• The x-intercept of the graph.

• The sign of the constant multiplier.

If a graph is multiplied by a negative constant, what additional transformation occurs?

• The graph reflects over the y-axis.

• The graph reflects over the x-axis.

• The graph shifts downwards.

• The graph shifts upwards.

In the example transformation, what does the term x - 2 represent?

• A horizontal shift to the left.

• A vertical shift upwards.

• A horizontal shift to the right.

• A vertical shift downwards.

What is the effect of the negative sign in the transformation example?

• It causes a vertical stretch.

• It causes a vertical shrink.

• It reflects the graph over the x-axis.

• It reflects the graph over the y-axis.

What is the final step in the transformation example provided?

• Shift the graph two units to the right.

• Shift the graph five units down.

• Reflect the graph over the x-axis.

• Apply a vertical shrink.

What is the first transformation applied in the example provided?

• Vertical shrink by a factor of 1/3.

• Reflection over the x-axis.

• Horizontal shift to the right.

• Vertical shift downwards.

Why is the order of operations important in graph transformations?

• To ensure the graph is shifted correctly.

• To apply transformations in the correct sequence.

• To determine the correct scale of the graph.

• To identify the correct intercepts.

How can you describe the overall transformation of the graph in the example?

• A vertical stretch followed by a horizontal shift.

• A reflection followed by a vertical stretch.

• A horizontal shift followed by a vertical shrink.

• A vertical shrink, reflection, horizontal shift, and vertical shift.