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 up affect its graph?

Back

Shifting a function up by k units adds k to the output values, moving the entire graph upward.

Front

How does shifting a function down affect its graph?

Back

Shifting a function down by k units subtracts k from the output values, moving the entire graph downward.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means to invert the output values, changing f(x) to -f(x).

Front

What does it mean to reflect a function over the y-axis?

Back

Reflecting a function over the y-axis means to invert the input values, changing f(x) to f(-x).

Front

What is the effect of shifting a function left by 3 units?

Back

Shifting a function left by 3 units subtracts 3 from the input values, moving the entire graph to the left.

Front

What is the effect of shifting a function right by 3 units?

Back

Shifting a function right by 3 units adds 3 to the input values, moving the entire graph to the right.

Front

How do you determine the horizontal asymptote of a reciprocal function?

Back

For reciprocal functions, the horizontal asymptote is typically y = 0 unless transformed.