Evaluating Polynomial Functions

The video tutorial explains function notation using the function g(x) = 2x^2. It demonstrates how to calculate the function for different values: g(4), g(-2), g(d), and g(5c). Each calculation is shown step-by-step, emphasizing the order of operations and the substitution of variables.

What is the function g(x) defined as in the video?

• g(x) = x^3

• g(x) = 2x^2

• g(x) = x^2

• g(x) = 3x^2

When evaluating g(4), what is the first step according to the order of operations?

• Divide 4 by 2

• Add 2 to 4

• Square 4

• Multiply 2 by 4

What is the result of g(4) when evaluated?

• 64

• 32

• 8

• 16

What is the result of multiplying 2 by 16 in the evaluation of g(4)?

• 8

• 32

• 64

• 16

When evaluating g(-2), why is the result positive?

• Because multiplication by 2 makes it positive

• Because squaring a number always results in a positive value

• Because the function is defined to be positive

• Because -2 is positive

What is the result of g(-2) when evaluated?

• -4

• 8

• 4

• -8

What is the significance of the order of operations in evaluating functions?

• It only applies to addition and subtraction

• It is not important

• It determines the final result

• It makes calculations faster

What does squaring a negative number result in?

• An undefined value

• A positive number

• Zero

• A negative number

How is the function g(d) expressed?

• g(d) = d^3

• g(d) = 2d^2

• g(d) = d^2

• g(d) = 2d

What is the purpose of replacing x with a variable like d in g(d)?

• To change the function's output

• To simplify the function

• To generalize the function for any input

• To make the function more complex