Understanding Function Notation

This video tutorial introduces function notation, explaining its significance in representing functions. It covers the concept of F of X, where F of X is the output from applying a function rule to input X. The tutorial provides examples, such as F of X = 2X + 3, and demonstrates how to find function values through substitution. It also explores examples with different functions like G of T and H of Y, including handling variable expressions as inputs.

What does the notation f(x) represent in function notation?

• The product of f and x

• The input of the function

• The sum of f and x

• The output of the function

If f(x) = 2x + 3, what is f(4)?

• 11

• 8

• 9

• 10

In the function f(x) = x^2 - 5x + 6, what is f(4)?

• 2

• 0

• 4

• 6

For the function f(x) = x^2 - 5x + 6, what is f(-3)?

• 24

• 15

• 30

• 9

What is the output of g(t) when t = -3 if g(t) = -t^2 + 2t - 12?

• -27

• -15

• -9

• -3

If g(t) = -t^2 + 2t - 12, what is g(3x)?

• 9x^2 + 6x - 12

• -9x^2 - 6x + 12

• 9x^2 - 6x + 12

• -9x^2 + 6x - 12

In the function h(y) = 2y^2 - y + 7, what is h(m-2)?

• 2m^2 - 9m + 15

• 2m^2 - 7m + 16

• 2m^2 - 8m + 15

• 2m^2 - 9m + 17

What is the first step in simplifying h(m-2) for h(y) = 2y^2 - y + 7?

• Divide m-2 by 2

• Subtract m from 2

• Add 7 to m-2

• Multiply m-2 by itself

What is the result of expanding (m-2)^2?

• m^2 - 4m - 4

• m^2 + 4m + 4

• m^2 - 2m + 4

• m^2 - 4m + 4

What is the final expression for h(m-2) in the function h(y) = 2y^2 - y + 7?

• 2m^2 - 9m + 15

• 2m^2 - 7m + 16

• 2m^2 - 8m + 15

• 2m^2 - 9m + 17