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Question 747682: (Hi... I'm Dannielle. 8th grade student taking Algebra1) I'm confused... on a preparation packet that's 10% of my grade... Lovely isn't it? Yet another thing my Algebra1 teacher never got the chance to teach. The question says: "A function of g is described : g(x)=(x-3)2 +6... The domain of g is all real numbers greater than 0. The range of g is all real numbers greater than or equal to - A.) 9, B.) 6, C.) 3, D.) -3... " Okay... correct me if I'm wrong, but does g(x) mean basically the same thing as the f(x) but the function is just labeled g instead of f? Yes? No? Sigh.. Okay. All I could think of doing was starting by factoring out the original equation but I just got x2-3x+15. I'm almost positive that I did that wrong and to be completely honest I'm not exactly sure that was what I was supposed to be doing to get the answer. Any suggestions or help would be greatly appreciated... (PS: I don't know if I'm asking this in the correct category so my apologies if this is the wrong one to be asking this is! )
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (Hi... I'm Dannielle. 8th grade student taking Algebra1) I'm confused... on a preparation packet that's 10% of my grade... Lovely isn't it? Yet another thing my Algebra1 teacher never got the chance to teach. The question says:
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"A function of g is described : g(x)=(x-3)^2 +6... The domain of g is all real numbers greater than 0. The range of g is all real numbers greater than or equal to - A.) 9, B.) 6, C.) 3, D.) -3... "
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Answer: (x-3)^2 can never be negative. It's smallest value is zero;
that occurs when x = 3
So the Domain is "All Real Numbers >= 3".
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Okay... correct me if I'm wrong, but does g(x) mean basically the same thing as the f(x) but the function is just labeled g instead of f? Yes? No?
Answer: Yes
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Cheers,
Stan H.
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Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! (Hi... I'm Dannielle. 8th grade student taking Algebra1) I'm confused... on a preparation packet that's 10% of my grade... Lovely isn't it? Yet another thing my Algebra1 teacher never got the chance to teach. The question says: "A function of g is described : g(x)=(x-3)2 +6... The domain of g is all real numbers greater than 0. The range of g is all real numbers greater than or equal to - A.) 9, B.) 6, C.) 3, D.) -3... " Okay... correct me if I'm wrong, but does g(x) mean basically the same thing as the f(x) but the function is just labeled g instead of f? Yes? No? Sigh.. Okay. All I could think of doing was starting by factoring out the original equation but I just got x2-3x+15. I'm almost positive that I did that wrong and to be completely honest I'm not exactly sure that was what I was supposed to be doing to get the answer. Any suggestions or help would be greatly appreciated... (PS: I don't know if I'm asking this in the correct category so my apologies if this is the wrong one to be asking this is! )
The smallest value of g(x) is when x = 3, as when 3 is substituted for x into the function, g(x) =  , we get: g(3) =  , which equals 6. Any other real number value, negative or positive, that's substituted will result in a larger value than 6.
Therefore, the range of g, or g(x) =  )(CHOICE B).
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