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Exponential and logarithmic functions with the same base are __________ because they undo each other. The...

Exponential and logarithmic functions with the same base are __________ because they undo each other.
The graph of a logarithmic function is reflected across the line __________ when compared to its related exponential function.
The parent logarithmic function \( f(x) = \log_b(x) \) has a vertical asymptote at __________ on the coordinate plane.
The parent logarithmic function has domain __________ because logarithms are only defined for positive input values.
When \( b > 1 \), the graph of \( f(x) = \log_b(x) \) is __________ as \( x \) increases.

Answer

  1. Exponential and logarithmic functions with the same base are inverse functions because they undo each other.

  2. The graph of a logarithmic function is reflected across the line y = x when compared to its related exponential function.

  3. The parent logarithmic function \( f(x) = \log_b(x) \) has a vertical asymptote at x = 0 on the coordinate plane.

  4. The parent logarithmic function has domain (0, ∞) because logarithms are only defined for positive input values.

  5. When \( b > 1 \), the graph of \( f(x) = \log_b(x) \) is increasing as \( x \) increases.

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