Transforming Algebraic Functions: Techniques for Graphing

Professor Dave explains how to transform functions by graphing basic functions like X squared and applying transformations such as vertical and horizontal shifts, stretches, and reflections. He demonstrates these transformations with examples, showing how to graph variations of functions by applying these transformations. The lesson concludes with a summary of the transformations and a note on handling more complex functions.

What is the shape of the graph for the function F(x) = x^2?

• A circle

• A hyperbola

• A parabola opening upwards

• A straight line

How does the graph of x^2 change when we add 2 to it, making it x^2 + 2?

• It shifts 2 units down

• It shifts 2 units up

• It shifts 2 units to the right

• It shifts 2 units to the left

What kind of shift occurs when we have (x + 2)^2?

• Vertical shift down

• Vertical shift up

• Horizontal shift to the left

• Horizontal shift to the right

What happens to the graph of x^2 when it is multiplied by 2, making it 2x^2?

• It shifts downwards

• It shifts upwards

• It becomes narrower

• It becomes wider

If the coefficient inside the term is less than 1, like (1/2)x^2, what happens to the graph?

• It shrinks horizontally

• It shrinks vertically

• It stretches vertically

• It stretches horizontally

What transformation occurs when the function is -x^2?

• Reflection across the Y axis

• Horizontal shift to the left

• Reflection across the X axis

• Horizontal shift to the right

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

• Horizontal shift to the right by 3

• Vertical shift up by 4

• Reflection across the X axis

• Vertical stretch by a factor of 2

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

• Vertical shift up by 4

• Horizontal shift to the right by 3

• Vertical stretch by a factor of 2

• Reflection across the X axis

How can we describe the graph of |x| - 2?

• Absolute value function shifted 2 units to the right

• Absolute value function shifted 2 units to the left

• Absolute value function shifted 2 units down

• Absolute value function shifted 2 units up

What should we do if a function cannot be reduced to a series of transformations?

• Transform it into a polynomial

• Graph it as is

• Use another strategy

• Ignore the function