Understanding Parent Functions and Graph Transformations

The video tutorial explains the concept of parent functions, focusing on the square root function. It covers how to graph transformations by applying horizontal and vertical shifts. The tutorial uses Desmos to demonstrate these transformations, providing a visual understanding of how equations change the graph's position.

What is a parent function?

• A function that has been transformed

• The original graph of a function

• A function with multiple variables

• A function that does not cross the origin

Which of the following is the parent function for a linear graph?

• y = x^2

• y = x^3

• y = x

• y = √x

What shape does the graph of y = x^2 take?

• A parabola

• A circle

• A straight line

• An S-curve

How does the graph of y = x^3 cross the origin?

• As a straight line

• As an S-curve

• As a parabola

• As a circle

What is the graphical representation of the parent function y = √x?

• Half a parabola sideways

• An S-curve

• A full parabola

• A straight line

What does a horizontal shift in a graph represent?

• Compressing the graph

• Movement up or down

• Movement left or right

• Stretching the graph

In the equation y = √(x - h) + k, what does 'h' represent?

• Y-intercept

• Slope

• Horizontal shift

• Vertical shift

If a graph is shifted 6 units to the left, what is the value of 'h' in the equation y = √(x - h) + k?

• 3

• -6

• 0

• 6

How do you represent a downward vertical shift of 3 units in the equation y = √(x - h) + k?

• k = -3

• k = 3

• h = -3

• h = 3

Which tool was used to verify the transformed equations in the video?

• Desmos

• GeoGebra

• Graphing calculator

• Mathematica