State the horizontal asymptote of the rational function f(x)= 7x^2-3x-9/2x^2-4x+5

The horizontal asymptote of a rational function exists when both numerator and denominator have the same degree, i.e. the same highest power.

The horizontal asymptote is the limiting case when x goes to +inf. or -inf.

The limit, when evaluated, reducces to the fraction formed by the leading coefficients of the numerator and denominator, meannig the fraction formed by the coefficient of the highest power.

In this case, the leading coefficients are respectively 7 and 2 for the numerator and denominator, hence the horizontal asymptote is 7/2=3.5.

See attach graph.

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.