Question #58f14

1 Answer
Ryuu
Sep 17, 2017

#"D:"# #{x inRR | x!=0}#
#"R":# #{y inRR | y!=-4}#

Explanation:

Domain and range are a set of values that the function can possibly have. It does not have to be at the same time.

Domain corresponds to the possible #x# values while range corresponds to the possible #y# values.

Because this function is a reciprocal, there are going to be two asymptotes. Normally, these asymptotes are the axes, but since the function was translated to the left 4 units, there will be a new asymptote.

The domain of the base function is #{x inRR | x!=0}#. The range of the base function is #{y inRR | y!=0}#.

With a single transformation applied (translated to the left 4 units), only the range is affected. The new range is #{y inRR | y!=-4}#.

If we graph the function, we can get a visual representation of the function.

graph{y=1/(x+4) [-8.89, 8.89, -4.45, 4.44]}

As you can see, the only value that the function cannot have is #(0, -4)#.

Hope this helps :)

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