Transforming Algebraic Functions: Shifting, Stretching, and Reflecting

The video tutorial explains how to transform functions graphically, focusing on vertical and horizontal shifts, stretches, and reflections. It covers how to apply these transformations to basic functions like x squared, and how to combine multiple transformations. The tutorial emphasizes understanding these transformations to easily graph variations of common functions.

What happens to the graph of f(x) = x^2 when you add a constant to the function, such as f(x) = x^2 + 2?

• The graph becomes narrower.

• The graph reflects over the x-axis.

• The graph shifts 2 units upwards.

• The graph shifts 2 units to the right.

How does the graph of f(x) = (x + 2)^2 differ from f(x) = x^2?

• It reflects over the y-axis.

• It shifts 2 units to the right.

• It shifts 2 units to the left.

• It becomes wider.

What is the effect of a coefficient greater than 1 in front of x^2, such as in f(x) = 2x^2?

• The graph becomes narrower.

• The graph shifts upwards.

• The graph reflects over the x-axis.

• The graph becomes wider.

If a function is given as f(x) = -x^2, what transformation occurs?

• The graph shifts to the left.

• The graph becomes wider.

• The graph reflects over the x-axis.

• The graph shifts downwards.

What is the result of applying a negative coefficient inside the squared term, such as in f(x) = (-x)^2?

• The graph shifts upwards.

• The graph reflects over the y-axis.

• The graph becomes narrower.

• The graph reflects over the x-axis.

In the function f(x) = -2(x - 3)^2 + 4, what is the first transformation applied?

• Vertical shift 4 units upwards.

• Horizontal shift 3 units to the left.

• Vertical stretch by a factor of 2.

• Reflection over the x-axis.

What is the final transformation applied to the function f(x) = -2(x - 3)^2 + 4?

• Reflection over the x-axis.

• Horizontal shift 3 units to the right.

• Vertical stretch by a factor of 2.

• Vertical shift 4 units upwards.