QZ MA Graphing Reciprocal Functions

Front

What is a reciprocal function?

Back

A reciprocal function is a function of the form f(x) = 1/x, where x is not equal to zero.

Front

What is the general shape of a reciprocal function graph?

Back

The graph of a reciprocal function has two branches, one in the first quadrant and one in the third quadrant, approaching the x-axis and y-axis asymptotes.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where a function approaches infinity or negative infinity as x approaches a.

Front

How do you find the vertical asymptote of a reciprocal function?

Back

Set the denominator of the function equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that the graph of a function approaches as x approaches infinity or negative infinity.

Front

What is the horizontal asymptote of the function f(x) = 1/x?

Back

The horizontal asymptote is y = 0.

Front

What does it mean to shift a graph left or right?

Back

Shifting a graph left or right involves adding or subtracting a value from the x-variable in the function.

Front

What does it mean to shift a graph up or down?

Back

Shifting a graph up or down involves adding or subtracting a value from the entire function.

Front

What is a transformation in graphing?

Back

A transformation is a change made to the graph of a function, such as shifting, stretching, or reflecting.

Front

What does it mean to stretch a graph vertically?

Back

Stretching a graph vertically means to multiply the function by a factor greater than 1, making it taller.