Transformations of 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

What is a horizontal asymptote?

Back

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

Front

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

Back

Shifting a function to the left by 'h' units means replacing x with (x + h) in the function's equation.

Front

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

Back

Shifting a function to the right by 'h' units means replacing x with (x - h) in the function's equation.

Front

How does shifting a function up affect its graph?

Back

Shifting a function up by 'k' units means adding 'k' to the function's output.

Front

How does shifting a function down affect its graph?

Back

Shifting a function down by 'k' units means subtracting 'k' from the function's output.

Front

What is the effect of multiplying a function by -1?

Back

Multiplying a function by -1 reflects the graph across the x-axis.

Front

What is the effect of multiplying a function by a positive constant greater than 1?

Back

Multiplying a function by a positive constant greater than 1 vertically stretches the graph.

Front

What is the effect of multiplying a function by a positive constant between 0 and 1?

Back

Multiplying a function by a positive constant between 0 and 1 vertically compresses the graph.