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How do you find the domain and range of #f(x) = (x + 8)^2 - 7#?

Answer 1

Inspect using the formula #y=a(x-h)^2+k#

From the equation given #f(x)=(x+8)^2-7# we can see that:

h = -8 and k = -7

From the original equation #y=x^2#, if h is negative the graph the will shift left or negative x and if k is negative the graph will shift down or negative y.

graph{(x+8)^2-7 [12.8, -8.72, 12.95, -27.05]}

Since x will keep increasing to infinity regardless of any x-axis transformations the domain will be the same as #y=x^2#

Domain: Every single real number

However, since a minimum applies to the range, if the graph shifts in the y-axis the range will be different from #y=x^2#

Range: y ≥ -7

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Answer 2

Jace Anderson

The domain of the function is all real numbers because there are no restrictions on the input ( x ). The range of the function is all real numbers greater than or equal to -7 because the function ( f(x) ) will always produce a value 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.