Understanding Functions and Their Applications

The video tutorial introduces the concept of functions, explaining them with real-life examples like babysitting jobs. It covers function notation, domain, and range, providing examples and practice problems to reinforce understanding. The tutorial emphasizes the importance of understanding functions as relationships between inputs and outputs, and how to determine domain and range from graphs and equations.

In the babysitting example, what does the equation 2x - 3 represent?

• The total earnings from babysitting

• The number of hours worked

• The number of kids attending

• The cost of renting the building

What is the function notation for y = x^2 + 5?

• y(x) = x^2 + 5

• h(x) = x^2 + 5

• g(x) = x^2 + 5

• f(x) = x^2 + 5

If f(x) = x^2 - 2x, what is f(4)?

• 12

• 8

• 16

• 4

What is the domain of the function f(x) = 2x?

• Only integers

• All positive numbers

• All real numbers

• All negative numbers

For the function f(x) = 3, what is the range?

• All negative numbers

• All positive numbers

• Only 3

• All real numbers

What is the domain of f(x) = 5 - √(5 - x)?

• x ≥ 5

• x ≤ 5

• x > 5

• x < 5

Which value cannot be used in the function f(x) = 1/x?

• 2

• 0

• 1

• -1

In the practice problems, what is the result of substituting m^2 into the function f(x) = 2x^2 + 3x - 5?

• 2m^4 + 3m^2 - 5

• 2m^2 + 3m - 5

• 2m^4 + 3m - 5

• 2m^2 + 3m^2 - 5

What is the domain of the function f(x) = 1/(x-1)?

• x = 1

• x ≠ 1

• x > 1

• x < 1

In the practice problems, what is the range of the function g(x) = 2?

• Only 2

• All negative numbers

• All real numbers

• All positive numbers