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4 votes
Find the range of y =
2^( x)

Find the range of y =
2 ^( - x)
Please help!​

2 Answers

5 votes

Explanation:

y = 2^x. y>0 is the range (0, ♾️)

y = 2^-x. y >0 is the range. (0, ♾️)

User Yochi
by
8.0k points
4 votes

Answer:

Range of y = 2^x is all positive real numbers.

Range of the function y = 2^{-x} is all positive real numbers excluding zero

Explanation:

Find the range of y = 2^x

Answer:

  • Since 2^x is an exponential function with a base of 2, the function will always output positive values.

This means that the range of y is all positive real numbers, or y > 0.

In mathematical notation, we can express the range as:


y \in (0, \infty)

Therefore, the range of y = 2^x is all positive real numbers .


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Find the range of y = 2^(-x)

Answer:

Since 2^{-x} represents the reciprocal of 2^x, the function will output positive values as the exponent becomes more negative.

  • As x approaches positive infinity
    x \to \infty, the value of 2^{-x} approaches 0.
  • As x approaches negative infinity
    x \to -\infty, the value of 2^{-x} approaches positive infinity.

Therefore, the range of the function y = 2^{-x} is all positive real numbers greater than zero, but does not include zero itself.

In mathematical notation, we can express the range as:


y \in (0, \infty)

Therefore, range of the function y = 2^{-x} is all positive real numbers excluding zero.

User Soham
by
8.5k points

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