Understanding the Domain of Linear Functions

The video tutorial explains how to find the domain of the linear function f(x) = 2x - 3. It begins by defining the domain as the set of all x values that make the function true. The instructor then graphs the function, highlighting its continuous nature without breaks, indicating that every x value has a corresponding y value. The video contrasts this with functions that have restrictions, such as f(x) = 1/x and f(x) = √x, which have limitations on their domains. The tutorial concludes that the domain of the given linear function is all real numbers, as it extends from negative infinity to positive infinity without restrictions.

What is the domain of the linear function f(x) = 2x - 3?

• Numbers greater than zero

• Only negative numbers

• Only positive numbers

• All real numbers

What does the y-intercept of the function f(x) = 2x - 3 represent on the graph?

• The point where the graph crosses the x-axis

• The slope of the graph

• The point where the graph crosses the y-axis

• The highest point on the graph

What is the slope of the function f(x) = 2x - 3?

• -3

• 3

• 2

• 1

What does it mean when a graph is continuous?

• It has breaks at certain points

• It extends infinitely without breaks

• It only exists in the first quadrant

• It is a closed shape

Which of the following functions has a domain restriction?

• f(x) = x + 5

• f(x) = 1/x

• f(x) = x^2

• f(x) = 2x - 3

Why can't x be zero in the function f(x) = 1/x?

• Because it would make the function undefined

• Because it would make the function zero

• Because it would make the function positive

• Because it would make the function negative

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

• Numbers greater than or equal to zero

• All real numbers

• Only negative numbers

• Only positive numbers

What is the range of the linear function f(x) = 2x - 3?

• All real numbers

• Only positive numbers

• Only negative numbers

• Numbers greater than zero

What happens to the graph of f(x) = 2x - 3 as x approaches infinity?

• It approaches a maximum value

• It becomes horizontal

• It approaches a minimum value

• It continues to rise indefinitely

What does it mean for a function to have no domain restrictions?

• It can take any real number as input

• It can only take integer values

• It can only take negative values

• It can only take positive values