What is the range of #y = 3x^2 - 7#?

Answer 1

An additional method is to observe that

#f(x)+7=3x^2>=0#
#f(x)+7>=0#
#f(x)>=-7#
Hence the range is #R_f=[-7,+oo)#
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Answer 2
Since your function is a quadratic and the quadratic coefficient is positively-signed, it has a single minimum value, and extends upwards towards #oo#.

Your lower bound is therefore reached when you've determined the smallest y value that's feasible.

Since the second degree term is not horizontally shifted (that is, #(x+c)^2#, where #c=0#), the minimum is when #x=0#.

Thus, your range is:

#color(blue)([-7", " oo ))#
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Answer 3

The range is all real numbers greater than or equal to -7.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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