It seems like there might be a typo or missing information in the equation you've provided. The expression \( y = 2** + 3 \) is not clear. If you're referring to a function like \( y = 2^x + 3 \) (an exponential function), then I can assist you with that.
Assuming the function is \( y = 2^x + 3 \), let's discuss its properties, including the horizontal asymptote.
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Horizontal Asymptote: For \( y = 2^x + 3 \), as \( x \) approaches negative infinity, \( 2^x \) approaches 0. Therefore, the horizontal asymptote is \( y = 3 \).
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Points on the Graph:
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To find the value \( a \) when \( x = 0 \): \[ y = 2^0 + 3 = 1 + 3 = 4. \] So, the point is \( (0, 4) \) and hence \( a = 4 \).
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To find the \( x \)-coordinate \( b \) when \( y = 3.5 \): \[ 3.5 = 2^x + 3. \] Subtracting 3 from both sides gives: \[ 0.5 = 2^x. \] Taking the logarithm base 2: \[ x = \log_2(0.5) = -1. \] Therefore, the point is \( (-1, 3.5) \), meaning \( b = -1 \).
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So, the answers are:
- \( a = 4 \)
- \( b = -1 \)
If this was not the function you intended to refer to, please provide the correct function or additional context!
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