Graph Transformations and Function Types

The video tutorial introduces function families, including constants, linear, absolute value, and quadratic functions. It explains graphing techniques and function notation, followed by a detailed discussion on transformations such as reflection, stretch, shrink, and translation. A template is provided to help analyze these transformations. The tutorial concludes with practical applications and assignments to reinforce learning.

What is the graphical representation of a constant function?

• A vertical line

• A horizontal line

• A curved line

• A diagonal line

Which of the following represents a linear function?

• f(x) = 1

• f(x) = x^2

• f(x) = |x|

• f(x) = x

What shape does the graph of an absolute value function resemble?

• A V-shape

• A straight line

• A U-shape

• A circle

What is the standard form of a quadratic function?

• f(x) = 1

• f(x) = |x|

• f(x) = x^2

• f(x) = x

What does a reflection over the x-axis do to a graph?

• Shrinks it horizontally

• Stretches it vertically

• Flips it top to bottom

• Flips it left to right

How does a vertical stretch affect a graph?

• Flips it over the y-axis

• Makes it narrower

• Makes it wider

• Moves it up

What is the effect of a reflection over the y-axis?

• Flips the graph top to bottom

• Flips the graph left to right

• Stretches the graph vertically

• Shrinks the graph horizontally

What does a horizontal translation do to a graph?

• Moves it up or down

• Stretches it vertically

• Moves it left or right

• Shrinks it horizontally

Which family does a graph with a V-shape belong to?

• Absolute Value

• Quadratic

• Linear

• Constant