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Someone help me on number 7 please

Someone help me on number 7 please-example-1

1 Answer

10 votes

Answer:

R: -9 < y < ∞

(option D)

Explanation:

So, the range of a function/relation is all possible y-values

(the domain is all possible x-values)

So, from looking at this graph, we can see where there is a y-value.

We can first ask ourselves: what is the highest possible y-value of this function?

Because there is an arrow approaching infinity, we can assume that the greatest possible y-value is ∞.

(note: our y < ∞ ; not ≤ ∞. This is because even though the y-value is approaching infinity, it can never truly be equal to infinity)

Next, we can observe: what is the lowest possible y-value of this function?

We can see that there is an asymptote {a curve constantly approaching, yet never reaching a value} at -9. This means that our y-value will never reach -9, so every possible y-value must be [at least slightly] greater than -9.

(note: our y > -9, not ≥ -9, because it is not possible for the y-value to truly be equal to -9)

So, if we combine this information:

y > -9

y < ∞

-9 < y < ∞

(We put R: in front of our range to signify that it is range--as opposed to domain)

Hope this helps!!

User Thomas B Homburg
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