Exploring Adding and Subtracting Rational Expressions

This video tutorial covers evaluating and graphing piecewise functions, both linear and non-linear. It begins with an introduction to piecewise functions, followed by detailed steps on how to evaluate them using specific function rules. The tutorial then demonstrates graphing techniques for these functions, including using x-y charts and understanding properties of parabolas. The video emphasizes understanding domain and range, and provides examples to illustrate these concepts.

What is the first step in evaluating a piecewise function?

• Substitute the value of x

• Simplify the equation

• Identify the domain rule

• Graph the function

If f(x) = -5x for x > 0, what is f(7)?

• -7

• 0

• 35

• -35

For g(x) = 4^x, what is g(-2)?

• 4

• 16

• 1/16

• 1/4

What is the value of h(-5) if h(x) = -11 + 3x for x < 1?

• -26

• -35

• -15

• -11

Which function rule should be used for f(-2) if x <= 0?

• f(x) = x^2

• f(x) = -5x

• f(x) = 4^x

• f(x) = 2x + 1

What is the value of g(-4) if g(x) = 16 - 4x - 7 for x < -2?

• 16

• -5

• -16

• 5

When graphing a piecewise function, what does a closed circle represent?

• The function is undefined at that point

• The function is continuous at that point

• The function is greater than at that point

• The function is less than at that point

What is the vertex of the parabola for f(x) = -2x^2 + 5 if x < 2?

• (0, 5)

• (1, 3)

• (2, -3)

• (3, -2)

For the function f(x) = x - 7, what is the y-intercept?

• 1

• 0

• 7

• -7

What is the domain of a piecewise function that extends all the way left and right?

• All positive numbers

• All integers

• All negative numbers

• All real numbers