Consider the function f (x) = (2x - a)(x - b)/5(x - b)(x - c). determine where the following features of its graph are located in terms of a, b, and/or c. explain your reasoning for each situation. a. the x-intercepts b. the y-intercepts c. any vertical asymptotes d. any horizontal asymptotes e. any “holes” in the graph

A) The function simplifies to
.. f(x) = (2x -a)/(5(x -c)) . . . . . . x ≠ b
The x-intercept will be located where f(x) = 0, at x = a/2.

b) The y-intercept is located where x = 0, at f(0) = a/(5c)

c) The vertical asymptote is where the denominator is zero, at x = c

d) The horizontal asymptote is the value that results when x gets large, y = 2/5.

e) There is a "hole" in the graph at x=b, where the function is undefined.