Exploring Adding and Subtracting Rational Expressions

This video tutorial introduces function families, focusing on linear and absolute value functions. It explains parent functions and demonstrates how to graph them. The tutorial covers transformations, including translation, dilation, and reflection, and shows how to apply these transformations using a graphing calculator. It also provides rules for identifying transformations and guides viewers in writing functions based on transformation descriptions.

Which of the following best describes a linear function?

• A function with a V-shaped graph

• A function with a parabolic graph

• A function with a straight-line graph

• A function with a circular graph

What is the parent function of a linear function?

• f(x) = x^2

• f(x) = |x|

• f(x) = 1/x

• f(x) = x

What is the parent function of an absolute value function?

• f(x) = x

• f(x) = |x|

• f(x) = x^2

• f(x) = 1/x

What does a transformation do to a function?

• Changes the color of the graph

• Changes the position or size of the graph

• Changes the type of function

• Changes the domain of the function

If the absolute value function f(x) = |x| is shifted left by 2 units, what is the new function?

• f(x) = |x + 2|

• f(x) = |x| - 2

• f(x) = |x| + 2

• f(x) = |x - 2|

What happens to the graph of f(x) = |x| when it is vertically stretched by a factor of 2?

• It shifts down

• It shifts up

• It becomes narrower

• It becomes wider

What is the effect of a negative sign in front of the absolute value function?

• It shifts the graph to the left

• It reflects the graph across the y-axis

• It shifts the graph to the right

• It reflects the graph across the x-axis

How would you describe the transformation of f(x) = |x| to f(x) = |x| - 3?

• Shifted right 3 units

• Shifted left 3 units

• Shifted down 3 units

• Shifted up 3 units

What is the new function if f(x) = |x| is vertically compressed by a factor of 1/4 and shifted left by 1 unit?

• f(x) = 4|x - 1|

• f(x) = 4|x + 1|

• f(x) = 1/4|x - 1|

• f(x) = 1/4|x + 1|

If f(x) = |x| is reflected across the x-axis and shifted up by 2 units, what is the new function?

• f(x) = |x| - 2

• f(x) = |x| + 2

• f(x) = -|x| + 2

• f(x) = -|x| - 2