Understanding Domains and Ranges in Trigonometric Functions

The video tutorial explains the concepts of domain and range in functions, including their graphical representation. It discusses constraints on domain and range, particularly in functions involving fractions and square roots. The video also covers the domain and range of trigonometric functions, highlighting specific constraints and asymptotes. Finally, it introduces the next video topics on inverse functions.

What is the domain of a function?

• The set of all possible input and output values

• The set of all possible output values

• The set of values that a function cannot accept

• The set of values that a function can accept as an argument

How does the range of a function relate to its graph?

• It corresponds to values along the vertical axis

• It is unrelated to the graph

• It is the same as the domain

• It corresponds to values along the horizontal axis

For the function f(x) = x + 1, what is the domain?

• All real numbers

• All positive numbers

• All negative numbers

• Only integers

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

• Only positive integers

• Real numbers less than zero

• Real numbers greater than or equal to zero

• All real numbers

Why is the function f(x) = 1/x constrained?

• Because x can be zero

• Because x cannot be zero

• Because x can be negative

• Because x must be positive

What is a general rule for domain constraints?

• When the variable is in the denominator or within a square root

• When the variable is a constant

• When the variable is in the numerator

• When the variable is an exponent

What is the domain of sine and cosine functions?

• Only positive numbers

• Only integers

• Only negative numbers

• All real numbers

What is the range of sine and cosine functions?

• Only positive numbers

• Between -2 and 2

• Between -1 and 1

• All real numbers

Why are cotangent and cosecant functions undefined at certain angles?

• Because cosine is zero at those angles

• Because sine is zero at those angles

• Because they have no asymptotes

• Because they are always defined

At which angles are cotangent and cosecant functions undefined?

• Multiples of pi/2

• Multiples of pi

• Multiples of 2pi

• Multiples of 3pi