Graphing Absolute Value Functions as Piecewise Functions

This video tutorial by Mr. Tarrou covers graphing absolute value functions as piecewise functions. It begins with an introduction to the relationship between absolute value and piecewise functions, highlighting their importance in calculus and real-world applications. The tutorial then provides detailed examples of graphing linear, rational, and quadratic functions with absolute values, explaining how to rewrite them as piecewise functions. Key concepts such as domain, range, and critical values are discussed, along with techniques for finding the vertex of a quadratic function.

Why is it important to understand the relationship between piecewise functions and absolute value functions in calculus?

• To simplify the process of finding derivatives and integrals.

• To understand the concept of limits.

• To graph polynomial functions.

• To solve linear equations more efficiently.

What is the shape of the graph for y = |x + 3|?

• A straight line

• A parabola

• A circle

• A V-shape

What is the critical value for the function y = |x + 3|?

• 1

• -3

• 0

• 3

In the function y = (x^2 + x - 2) / |x - 1|, what happens when x = 1?

• The function equals negative one.

• The function equals one.

• The function equals zero.

• The function is undefined.

How do you handle the absolute value in the denominator of y = (x^2 + x - 2) / |x - 1| for x > 1?

• Replace it with a negative parenthesis.

• Replace it with zero.

• Drop the absolute value symbols.

• Replace it with a positive parenthesis.

What is the domain of the function y = (x^2 + x - 2) / |x - 1|?

• All real numbers

• All real numbers except x = 1

• All positive numbers

• All negative numbers

What are the critical values for the function y = |x^2 - 4x - 5|?

• -1 and 5

• 2 and -2

• 1 and -5

• 0 and 4

How does the absolute value affect the graph of y = |x^2 - 4x - 5| between the critical values?

• It shifts the graph to the right.

• It reflects the graph above the x-axis.

• It makes the graph a straight line.

• It shifts the graph to the left.

What is the range of the function y = |x^2 - 4x - 5|?

• All negative numbers

• All non-negative numbers

• All positive numbers

• All real numbers

Which method can be used to find the vertex of a quadratic function?

• Completing the square

• Using the quadratic formula

• Graphing by hand

• Using a calculator