Explore

Reciprocal Functions Solutions

• A reciprocal function is a simple rational function in the form: $f\left(x\right)=\frac{a}{x–h}+k, x\ne h$

Note

The graph of $y=\frac{1}{x}$ may also be called an inverse function.

Note

Horizontal asymptotes also determine end behavior. You will learn about oblique (slant) asymptotes, how they occur, and end behavior in later lessons and levels.

• • An    asymptote    is a line that a graph (or curve) approaches (but does not touch) as it moves towards infinity or negative infinity.

• • The asymptote is drawn on a graph using a    dashed    line. It is used to help create    boundaries    for a function, but is not part of the graph itself.

• In a reciprocal function:

  • there is a    vertical    asymptote that is the restriction for the denominator, or domain.

  • there is one    horizontal   , asymptote, k.

  • a    never equals zero   . If $a=0$, it cannot be a reciprocal function.

•  If intercepts exist on the graph of a reciprocal function, then:


  • the x-intercepts, or zeros, of the graph are the values that make     f (x) = 0   .

  • the y-intercept is the value for     f(0)   .