Alg 2; Ch 8 1/8; Do Now

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It indicates that the function is undefined at that point.

x = -3

A horizontal asymptote is a line y = b where a function approaches b as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values of x.

y = 0

Adding a constant shifts the graph vertically. For example, f(x) = $$\frac{1}{x} + 3$$ shifts the graph up 3 units.

The negative sign reflects the graph across the x-axis.

Vertical asymptote: x = -2; Horizontal asymptote: y = -5.

Set the denominator equal to zero and solve for x.

It means the function is defined for all real numbers, and the denominator does not equal zero for any x.

It indicates a value of x where the function is undefined and where the function's behavior changes dramatically.