Exploring Parent Functions and Transformations

The video tutorial covers transformations of logarithmic and cubic functions, including flips across axes. It explains graphing circles, ellipses, and hyperbolas, focusing on identifying centers, radii, and stretches. The tutorial also highlights the differences between these shapes and provides guidance on using Desmos for hyperbolas.

What transformation is applied to the logarithmic function to flip it across the x-axis?

• Shifting the function to the right

• Multiplying the function by a negative sign

• Adding a constant to the function

• Shifting the function to the left

In the cubic function example, what is the result of flipping the graph across the y-axis?

• The graph flips horizontally

• The graph shifts down

• The graph flips vertically

• The graph shifts up

When graphing a circle, what does the term (x - h)^2 represent?

• The horizontal translation

• The vertical translation

• The diameter of the circle

• The radius of the circle

In the equation of a circle, what does the radius represent?

• The distance from the center to the origin

• The distance from one edge of the circle to the other

• The distance from the center to the edge of the circle

• The distance from the center to any point on the circle

What is the center of an ellipse represented by in its equation?

• h and k

• m and n

• a and b

• x and y

In the equation of an ellipse, what does the term (y - k)^2 represent?

• The horizontal stretch

• The vertical translation

• The vertical stretch

• The horizontal translation

What is the key difference between the equations of an ellipse and a hyperbola?

• The presence of a plus sign in the ellipse equation

• The presence of a minus sign in the ellipse equation

• The presence of a plus sign in the hyperbola equation

• The presence of a minus sign in the hyperbola equation

In a hyperbola, what does the term 'a' represent?

• The vertical stretch

• The horizontal stretch

• The slope of the curve

• The center of the hyperbola

What is the center of the circle in the practical example provided?

• (2, 6)

• (6, 4)

• (6, 2)

• (4, 2)

In the practical example of the ellipse, what is the horizontal stretch value?

• 2

• 3

• 4

• 5