Evaluating Piecewise-Defined Functions

The video tutorial explains piecewise functions, which can be represented graphically or algebraically. It describes how these functions are defined based on different conditions for the variable X. The tutorial provides examples using two functions, f and G, to demonstrate how to determine the function's value for specific X values. The key takeaway is understanding how to identify the correct piece of the function to use based on the value of X.

What are the two main ways to represent piecewise functions?

• Algebraically and verbally

• Graphically and algebraically

• Graphically and numerically

• Numerically and verbally

How many conditions are typically checked in a piecewise function?

• One

• Four

• Two

• Three

If x is less than zero, which part of the piecewise function is used?

• The third part

• The second part

• None of the above

• The first part

What is the value of f(-5) if the function is defined as f(x) = -1 for x < 0?

• 1

• -1

• 0

• -5

For x = 3, which condition of the piecewise function is satisfied?

• None of the above

• x < 0

• x ≥ 3

• 0 ≤ x < 3

What is the value of f(3) if the function is defined as f(x) = 15 for x ≥ 3?

• 15

• 7

• 9

• 3

In the function G(x), what is the value of G(-5) if G(x) = 2x - 1 for x < 3?

• -9

• -11

• -7

• -5

For x = 3, what is the value of G(3) if G(x) = x^2 + 7 for x ≥ 3?

• 14

• 10

• 12

• 16

What is the key step in evaluating a piecewise function?

• Directly substituting the value of x

• Using all parts of the function

• Checking which condition x satisfies

• Ignoring the conditions

Why is it called a piecewise function?

• Because it is a single equation

• Because it has only one condition

• Because it is continuous

• Because it is defined in pieces