Evaluating Functions and Expansions

The video tutorial explains how to evaluate a function of two variables at different points. It covers the substitution process for specific values and variables, simplifying expressions, and expanding binomials. The tutorial demonstrates evaluating f(a, -8), f(y, x), and f(x+h, y+h), highlighting the importance of substitution, simplification, and expansion in function evaluation.

What is the first step in evaluating f(a, -8)?

• Substitute -8 for both x and y

• Substitute a for both x and y

• Substitute a for y and -8 for x

• Substitute a for x and -8 for y

After substituting values in f(a, -8), what is the next step?

• Multiply all terms

• Simplify the expression

• Add all terms together

• Divide all terms by 2

When finding f(y, x), what substitution is made?

• x for y and y for x

• y for x and x for y

• No substitution is needed

• x for x and y for y

What is the simplified form of f(y, x)?

• y^2 + x^2 - 2x + 7

• x^2 + y^2 - 2y + 7

• y^2 + x^2 - 2y + 7

• x^2 + y^2 - 2x + 7

What is the first step in evaluating f(x+h, y+h)?

• Substitute x+h for x and y+h for y

• Substitute x+h for y and y+h for x

• Substitute y+h for both x and y

• Substitute x+h for both x and y

What is the purpose of expanding f(x+h, y+h)?

• To simplify the expression

• To find the derivative

• To write the function in expanded form

• To solve for h

Which term is not part of the expanded form of f(x+h, y+h)?

• 2h^2

• 2xy

• 2hx

• 2hy

What is the coefficient of h^2 in the expanded form of f(x+h, y+h)?

• 4

• 3

• 2

• 1

What happens to the function when one of the inputs is a variable?

• The output is a constant

• The output is another function

• The output is zero

• The output is undefined

What is the final step in the video?

• Solving a new example

• Introducing a new function

• Summarizing the examples

• Reviewing the expanded form