24. \( f(x)=\log _{1.2} x \)

The function \( f(x) = \log_{1.2} x \) is a logarithmic function with a base of \( 1.2 \). Here are some key points about this function: 1. **Domain**: The domain of \( f(x) \) is \( x > 0 \) because the logarithm is only defined for positive values of \( x \). 2. **Range**: The range of \( f(x) \) is all real numbers, \( (-\infty, \infty) \), since logarithmic functions can take any real value. 3. **Behavior**: - As \( x \) approaches \( 0^+ \) (from the right), \( f(x) \) approaches \( -\infty \). - As \( x \) increases, \( f(x) \) increases without bound, approaching \( +\infty \). 4. **Intercept**: The function has an x-intercept at \( x = 1 \) because \( \log_{1.2}(1) = 0 \). 5. **Increasing/Decreasing**: Since the base \( 1.2 \) is greater than 1, the function is increasing. This means that as \( x \) increases, \( f(x) \) also increases. 6. **Graph**: The graph of \( f(x) \) will pass through the point \( (1, 0) \) and will rise gradually as \( x \) increases. If you have any specific questions or need further analysis regarding this function, feel free to ask!