To determine which of the following functions is an example of a rational function, let's review each option provided:
1. [tex]\( f(x) = 270(1.01)^x \)[/tex]
This is an exponential function because it represents a constant base (1.01) raised to a variable exponent [tex]\( x \)[/tex].
2. [tex]\( g(x) = \frac{x^2 - 5x + 7}{x - 3} \)[/tex]
This is a rational function because it is the ratio of two polynomials. The numerator is [tex]\( x^2 - 5x + 7 \)[/tex] and the denominator is [tex]\( x - 3 \)[/tex].
3. [tex]\( h(x) = |x + 2| \)[/tex]
This is an absolute value function, which represents the distance of [tex]\( x + 2 \)[/tex] from zero on the real number line. It is not a rational function.
4. [tex]\( p(x) = \log_4(x)^3 \)[/tex]
This is a logarithmic function that has been raised to the power of 3. While it is a transformed logarithmic function, it is not a rational function either.
Based on this analysis, we can conclude the correct answer to be:
[tex]\[ \boxed{g(x) = \frac{x^2 - 5x + 7}{x - 3}} \][/tex]
This is the rational function among the given options.
