Question

which type of function describes f(x)? exponential logarithmic polynomial rational

Explanation:

A rational function is a ratio of two polynomials, and it often has vertical asymptotes (the red vertical line here suggests a vertical asymptote). Exponential functions have smooth growth/decay without asymptotes like this. Logarithmic functions have a vertical asymptote but their shape is different (increasing/decreasing slowly near the asymptote). Polynomial functions (like linear, quadratic) have no vertical asymptotes. So the function is likely rational.

Answer:

D. Rational