Writing Rational Functions

Question

Write an equation to match the function.

vertical asymptote: x = 4

slant asymptote: y = 2x

Create a function that matches the graph --- on the graph I see one line crosses through the point (5, 0). The other line passes through (-1, 0) and (0, 2.5).

I do not know how to write this function, can someone please help?

Answer 1

The answer is 2(x-5)(x+1)/(x-4)

The 2x² in the numerator with the x in denominator gives what you have called a slant asymptote of 2x.

The two factors in the numerator give you the 2 zeros and the numerator is -10 and the denominator is -4 when x=0.