Understanding Function Behavior and Properties

The video tutorial covers factoring trinomials, identifying discontinuities such as holes and asymptotes, simplifying functions, and graphing linear functions with holes. It also discusses determining the domain and range of functions with discontinuities and explores limits and continuity in calculus.

What is the first step in determining if a trinomial is factorable?

• Find the derivative

• Attempt to factor it

• Check for common factors

• Graph the trinomial

What happens to a discontinuity when it divides out?

• It disappears completely

• It remains unchanged

• It becomes a hole

• It becomes a vertical asymptote

Where does the hole occur in the function f(x) = (x+3)(x-1)/(x+3)?

• x = 1

• x = -1

• x = 3

• x = -3

What is the simplified form of the function after factoring and canceling out the hole?

• f(x) = x + 1

• f(x) = x - 3

• f(x) = x + 3

• f(x) = x - 1

What is the restriction on the function f(x) = x - 1?

• x cannot equal 1

• x cannot equal 3

• x cannot equal -1

• x cannot equal -3

In graphing the function, what is the slope of the line y = x - 1?

• 0

• 1

• -1

• 2

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

• (0, -1)

• (-1, 0)

• (0, 1)

• (1, 0)

What is the y-intercept of the function f(x) = x - 1?

• (1, 0)

• (0, 1)

• (0, -1)

• (-1, 0)

What is the domain of the function considering the hole?

• All real numbers

• All real numbers except x = 3

• All real numbers except x = -3

• All real numbers except x = 1

What is the range of the function considering the hole?

• All real numbers

• All real numbers except y = -4

• All real numbers except y = 3

• All real numbers except y = 1