Question

The range of which function is (2.oo)?
y = 2x
y = 2(5x)
y=5X +2
y = 5x + 2
​

Answer 1

Answer: $y = 5^x+2$

The 2 is not in the exponent.

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Explanation:

As x gets smaller and smaller, going off into the negative direction forever, the expression $5^x$ will approach 0. This is because we're computing stuff like 5^(-1) = 1/5 = 0.2 and 5^(-2) = 1/25 = 0.04 and so on. The decimal values are approaching 0 but never actually arrive there. The range of $y = 5^x$ is $(0,\infty)$

Adding on the 2 at the end will shift everything up so that the range is now $(2,\infty)$. Refer to the graph below.

The parenthesis in interval notation mean we do not include that endpoint as part of the set. Saying something like $(2,\infty)$ is the same as saying $2 < y <\infty$ when talking about the range.