Understanding Domain and Range

This video tutorial covers how to find the domain and range of functions using graphs and equations. It includes examples of linear, quadratic, radical, rational, trigonometric, exponential, and logarithmic functions. The video explains how transformations affect domain and range and provides strategies for identifying these from different types of functions.

What is the domain of a function that has a closed circle at x = 3 and an open circle at x = -3?

• (-3, 3)

• [-3, 3]

• (-3, 3]

• [-3, 3)

How does a vertical asymptote at x = 2 affect the domain of a function?

• The domain is unaffected by x = 2

• The domain is only x = 2

• The domain excludes x = 2

• The domain includes x = 2

For a polynomial function with an odd leading coefficient, what can be said about its range?

• The range is only positive numbers

• The range is all real numbers

• The range is limited

• The range is only negative numbers

What is the domain of the function y = √(x - 2) + 1?

• (2, ∞)

• (-∞, 2]

• (-∞, ∞)

• [2, ∞)

How does the transformation y = √(x + 3) - 4 affect the graph's starting point?

• Shifts 3 units left and 4 units down

• Shifts 3 units right and 4 units up

• Shifts 3 units right and 4 units down

• Shifts 3 units left and 4 units up

What is the domain of a function with a square root when the index is even?

• Values where the expression inside the square root is non-negative

• Values where the expression inside the square root is zero

• All real numbers

• Values where the expression inside the square root is negative

How do you determine the vertical asymptote of a rational function?

• Find where the numerator and denominator are equal

• Find the highest degree term in the numerator

• Set the denominator equal to zero

• Set the numerator equal to zero

What is the range of an exponential function with a horizontal asymptote at y = 1?

• Negative infinity to 1

• 0 to infinity

• 1 to infinity

• Negative infinity to 0

For a logarithmic function, how is the domain determined?

• Set the inside of the log equal to zero

• Set the inside of the log less than zero

• Set the base of the log greater than zero

• Set the inside of the log greater than zero

What is the range of a sine function with an amplitude of 3 and a vertical shift of 2?

• -1 to 5

• 2 to 5

• -3 to 3

• -5 to 1