Question
How to find range of g(x)=2^x-3
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GPT 3.5
To find the range of the function g(x) = 2^x - 3, we need to determine the set of all possible values that the function can output.
First, let's consider the function 2^x. The range of the exponential function 2^x is all positive real numbers, since 2 raised to any real power will always result in a positive value.
Next, we subtract 3 from 2^x to get g(x) = 2^x - 3. By subtracting 3 from all positive real numbers, we shift the range down by 3 units. Therefore, the range of g(x) = 2^x - 3 will be all real numbers less than -3.
In interval notation, the range of g(x) = 2^x - 3 is (-∞, -3). This means that g(x) can output any real number less than -3.
First, let's consider the function 2^x. The range of the exponential function 2^x is all positive real numbers, since 2 raised to any real power will always result in a positive value.
Next, we subtract 3 from 2^x to get g(x) = 2^x - 3. By subtracting 3 from all positive real numbers, we shift the range down by 3 units. Therefore, the range of g(x) = 2^x - 3 will be all real numbers less than -3.
In interval notation, the range of g(x) = 2^x - 3 is (-∞, -3). This means that g(x) can output any real number less than -3.
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