Graph Transformations and Properties

The video tutorial covers various mathematical functions and their transformations, including vertical and horizontal flips, shifts, and the effects on domain and range. It explains transformations of square root, hyperbola, logarithmic, absolute value, semicircle, and cube root functions, highlighting key concepts like intercepts, asymptotes, and symmetry.

What happens to a graph when it is flipped vertically?

• It reflects over the y-axis.

• It moves upwards.

• It reflects over the x-axis.

• It moves to the left.

Why is it important to label horizontal asymptotes on a graph?

• To identify the graph's intercepts.

• To determine the graph's domain.

• To calculate the graph's range.

• To understand the graph's end behavior.

How does a negative sign inside a square root function affect its graph?

• It flips the graph horizontally.

• It shifts the graph to the left.

• It flips the graph vertically.

• It shifts the graph upwards.

What is the domain of the transformed square root function 4 - x?

• x is greater than 4

• x is less than or equal to 4

• x is equal to 4

• x is not equal to 4

How does shifting a hyperbola horizontally affect its graph?

• It changes the graph's intercepts.

• It alters the graph's vertical asymptotes.

• It modifies the graph's horizontal asymptotes.

• It affects the graph's domain.

What is the significance of intercepts in a hyperbola transformation?

• They indicate the graph's symmetry.

• They define the graph's domain.

• They determine the graph's range.

• They serve as points for scale.

How does a horizontal shift affect an absolute value function?

• It affects the graph's vertical stretch.

• It moves the graph left or right.

• It alters the graph's symmetry.

• It changes the graph's slope.

What is the domain of an absolute value function shifted to the right?

• x is equal to zero

• x is less than zero

• x is greater than zero

• All real values of x

What is unique about the cube root function compared to the square root function?

• It cannot handle negative numbers.

• It has even symmetry.

• It can handle negative numbers.

• It grows faster than the square root function.

What kind of symmetry does the cube root function exhibit?

• Rotational symmetry

• Odd symmetry

• No symmetry

• Even symmetry