Graphing Reciprocal Functions

Front

What is a reciprocal function?

Back

A reciprocal function is a function of the form f(x) = 1/x, where the output is the reciprocal of the input.

Front

What is a vertical asymptote?

Back

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

Front

How does shifting a function to the left affect its graph?

Back

Shifting a function to the left by 'h' units means that every point on the graph moves 'h' units left, changing the function to f(x + h).

Front

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

Back

The range of f(x) = 1/x is all real numbers except for 0.

Front

What does it mean to stretch a function vertically?

Back

Stretching a function vertically means multiplying the function by a factor greater than 1, which increases the distance of points from the x-axis.

Front

What is a horizontal asymptote?

Back

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

Front

Describe the transformation: f(x) = 1/(x - 2).

Back

This function is shifted right by 2 units compared to the basic reciprocal function f(x) = 1/x.

Front

What happens to the graph of f(x) = 1/x when x approaches 0?

Back

As x approaches 0, f(x) approaches infinity or negative infinity, indicating a vertical asymptote at x = 0.

Front

What is the effect of a negative sign in front of a reciprocal function?

Back

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

Front

How do you find the vertical asymptote of f(x) = 1/(x + 2)?

Back

Set the denominator equal to zero: x + 2 = 0, which gives the vertical asymptote at x = -2.