Unit 3A/3B Test Review

Front

What is the equation of the reciprocal parent function?

Back

f(x) = 1/x

Front

How do you represent a translation of the reciprocal function right 3 and down 4?

Back

f(x) = 1/(x-3) - 4

Front

What is a vertical asymptote in the context of the reciprocal function?

Back

A vertical asymptote is a line that the graph approaches but never touches, typically where the function is undefined. For the reciprocal function, it occurs at x = 0.

Front

What is a horizontal asymptote in the context of the reciprocal function?

Back

A horizontal asymptote is a line that the graph approaches as x approaches infinity or negative infinity. For the transformed reciprocal function, it is y = -4.

Front

What is the domain of the reciprocal function after translating it left 5 and up 2?

Back

The domain is {x | x ≠ -5}.

Front

What happens to the vertical asymptote when the reciprocal function is translated right 3 units?

Back

The vertical asymptote moves from x = 0 to x = 3.

Front

What happens to the horizontal asymptote when the reciprocal function is translated down 4 units?

Back

The horizontal asymptote moves from y = 0 to y = -4.

Front

What is the significance of the vertical asymptote in the graph of a function?

Back

It indicates the values of x for which the function is undefined and helps in understanding the behavior of the function near those values.

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the denominator, y = 0. If they are equal, y = leading coefficient of numerator / leading coefficient of denominator.

Front

What is the effect of translating a function on its domain and range?

Back

Translating a function shifts its graph horizontally and/or vertically, which can change its domain and range depending on the direction and magnitude of the translation.