Graph Transformations and Effects

This video tutorial introduces the concept of parent functions and their transformations. It covers the basic parent functions such as quadratic, cubic, square root, reciprocal, and absolute value functions. The video explains how transformations like vertical stretch, vertical shrink, reflection, and horizontal shifts affect these functions. It provides four detailed examples demonstrating the transformation process for quadratic, cubic, square root, and cube root functions, highlighting the changes in their graphs.

Which of the following is a characteristic of a quadratic parent function?

• It is a straight line.

• It is a circle.

• It has a V-shaped graph.

• It has a U-shaped graph.

What happens to a graph when the parameter 'a' is greater than 1?

• The graph undergoes a vertical stretch.

• The graph shifts to the left.

• The graph shrinks vertically.

• The graph reflects over the x-axis.

In the transformation y = 2(x - 1)^2 + 3, what is the effect of the '-1' inside the parentheses?

• It shifts the graph up by 1 unit.

• It shifts the graph to the right by 1 unit.

• It shifts the graph down by 1 unit.

• It shifts the graph to the left by 1 unit.

In the transformation y = -2(x + 2)^3 + 4, what does the negative sign in front of the 2 indicate?

• The graph is shifted to the right.

• The graph is stretched vertically.

• The graph is reflected over the x-axis.

• The graph is shifted up.

What is the effect of a vertical shrink on a graph?

• It shifts the graph to the right.

• It makes the graph narrower.

• It shifts the graph to the left.

• It makes the graph wider.

In the transformation of a square root function, what does a vertical stretch by a factor of 3 do?

• It shifts the graph down by 3 units.

• It multiplies all x-values by 3.

• It shifts the graph up by 3 units.

• It multiplies all y-values by 3.

How does the parameter 'k' affect the graph of a function?

• It affects the reflection over the y-axis.

• It affects the reflection over the x-axis.

• It affects the vertical shift.

• It affects the horizontal shift.

In the transformation y = 3√(x + 3), what is the effect of the '+3' inside the square root?

• It shifts the graph to the left by 3 units.

• It shifts the graph up by 3 units.

• It shifts the graph to the right by 3 units.

• It shifts the graph down by 3 units.

What is the parent function of y = -2√(x) + 3?

• Reciprocal function

• Square root function

• Cubic function

• Quadratic function

What is the effect of a negative 'a' value in a transformation?

• It stretches the graph vertically.

• It reflects the graph over the x-axis.

• It shrinks the graph horizontally.

• It shifts the graph to the right.