To analyze the exponential function, let's consider it in a general form, such as \( y = a \cdot b^x \).
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Y-Intercept: The y-intercept of an exponential function occurs when \( x = 0 \). So, we can find the y-intercept by evaluating the function at \( x = 0 \): \[ y = a \cdot b^0 = a \] Thus, the y-intercept is simply \( (0, a) \).
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Asymptote: The horizontal asymptote of an exponential function is usually \( y = 0 \) for functions of the form \( y = a \cdot b^x \) (where \( a \) is a constant and \( b \) is a positive constant). This means that as \( x \) approaches negative infinity, \( y \) approaches 0.
Based on your options, it seems you're looking for specific selections:
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The y-intercept is: It could be any of the values provided (like (0, 1), (0, 5), etc.), but without more context about the specific function, we cannot determine it definitively.
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The equation of the asymptote is: The answer here is \( y = 0 \).
So, to complete the statement:
- The y-intercept is Select one of the y-intercept values you have.
- The equation of the asymptote is y = 0.
1 answer