SOLUTION: Which option below best describes why the domain of g(x) = 5–x is all real numbers but the range of g is not all real numbers?
1.The domain of g is all real numbers because ever
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Question 1087365: Which option below best describes why the domain of g(x) = 5–x is all real numbers but the range of g is not all real numbers?
1.The domain of g is all real numbers because every real number ________.
2.However, the range of g is not all real numbers because the ____________.
for question 1 their's two options which are :
-make sense as an exponent
-is an output of g
for question 2 their's also 2 options which are:
-exponent of g has a minus sign
-power of a positive real number
Please help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
It sounds like the given function is where the "-x" portion is the exponent. If so, then the domain of g is all real numbers because every real number makes sense as an exponent. In other words, there are no restrictions because there are no things like dividing by zero or taking the square root of a negative number to worry about.
As for the second part, it's not so clear. Something seems missing. The part "exponent of g has a minus sign" isn't the reason why the range is the set of positive numbers. The only thing left is "power of a positive real number" which makes a bit of sense, but it's not a complete sentence. It seems like it has been cut off. Please repost the full problem with that part not cut off, if you can. Thank you.
As a side note, here is the graph of g(x)
Keep in mind that the graph NEVER touches the x axis. It simply gets closer and closer to the asymptote. The expression 5^(-x) will never equal zero no matter how big x gets.
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