Grpah, identify the domain, range and compare the graph with the graph of y=1/x 1A) y=-10/x   Domain   Range    Compare B) y= 1/x+3 +3   Domain   Range   Compare  This is what the...

Grpah, identify the domain, range and compare the graph with the graph of y=1/x

1A) y=-10/x

Domain

Range

Compare

B) y= 1/x+3 +3

Domain

Range

Compare

This is what the graph looks like for A and B

Thank you.

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted on

The domain of a function is defined as all possible values of x.
The range of a function is defined as all possible values of y.

A)` f(x)=-10/x`

Domain: x can be all values except 0, for which the function is undefined.  Therefore the domain is x>0 and x<0.

Range: y is all values except 0, because no value of x will make -10/x = 0.  Therefore the range is y>0 and y<0

Compared to 1/x (black), -10/x (blue) is scaled by a factor of 10, and rotated about the origin by 90 degrees.

B) `f(x)=1/(x+3)+3 = (1+3(x+3))/(x+3)=(3x+4)/(x+3)`

Domain: x can be any value except -3, for which the function is undefined.  Therefore the domain is x>-3 and x<-3

Range: y is any value other than 3, because no value of x will make (3x+4)/(x+3) = 3.  Therefore the range is y>3 and y<3

Compared to 1/x (black), (3x+4)/(x+3) (blue) is rotated about the origin by 90 degrees, is shifted in x by 3 units to the left, and shifted in y by 3 units up.

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