Reciprocal Graphs

 In the graph of  $y=f\left(x\right)$  , $x=2$  is a vertical asymptote. For the graph of  $y=\frac{1}{f\left(x\right)}$  ,

•  $x=2$  is still an asymptote.

•  $y=0$  Is an asymptote.

• (2,0) is an intercept.

• x=1/2 is an asymptote.

Tags

CCSS.HSF-IF.C.7D

 In the graph of  $y=f\left(x\right)$  , $y=3$  is a horizontal asymptote. For the graph of  $y=\frac{1}{f\left(x\right)}$  ,

•  $y=\frac{1}{3}$  is an asymptote.

•  $y=3$  is still an asymptote.

• The horizontal asymptote will disappear.

Tags

CCSS.HSF-IF.C.7D

 In the graph of  $y=f\left(x\right)$  , $y=2x-1$  is an oblique asymptote. For the graph of  $y=\frac{1}{f\left(x\right)}$  ,

•  $y=0$  is an asymptote.

•  $y$  approaches  $\pm\infty$  .

• all asymptotes will disappear.

Tags

CCSS.HSF-IF.C.7D

 In the graph of  $y=f\left(x\right)$  , $\left(-3,0\right)$  is an x-intercept.  For the graph of  $y=\frac{1}{f\left(x\right)}$  ,

•  $\left(-\frac{1}{3},0\right)$  is an x-intercept.

•  $x=-3$  Is a vertical asymptote. 

•  $y=-3$  is an asymptote.

Tags

CCSS.HSF-IF.C.7A

 In the graph of  $y=f\left(x\right)$  , $\left(0,b\right)$  is a y-intercept.  For the graph of  $y=\frac{1}{f\left(x\right)},$   $\left(0,\frac{1}{b}\right)$  is a y-intercept. 

• This is always true because ___________.

• This is always false because ___________.

• This is true only if ____________.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

 In the graph of  $y=f\left(x\right)$  , $\left(2,4\right)$  is a maximum turning point.  For the graph of  $y=\frac{1}{f\left(x\right)}$  ,

•  $\left(2,\frac{1}{4}\right)$  is a maximum turning point. 

•  $\left(2,4\right)$  is a maximum turning point. 
  

•  $\left(2,\frac{1}{4}\right)$  is a minimum turning point.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

 In the graph of  $y=f\left(x\right)$  , $f\left(x\right)\rightarrow\pm\infty$  as  $x\rightarrow\pm\infty.$ For the graph of  $y=\frac{1}{f\left(x\right)}$  ,

• the graph has an x-intercept  $\left(a,0\right)$  .

• the graph still approaches  $\pm\infty.$  

•  $y=0$  Is a horizontal asymptote.
  

If  $f\left(x\right)>0,$   $\frac{1}{f\left(x\right)}>0.$  

• False

• True

Tags

CCSS.HSA-SSE.A.1A

In the graph of  $y=f\left(x\right),$  the curve is increasing. For the graph of  $y=\frac{1}{f\left(x\right)},$  the curve is also increasing.

• False

• True