Answer:
To find the x and y intercepts of the rational function f(x) = (3x-4) / (2x+3)(2x+5), we need to solve for the values of x and y that make the numerator or the denominator zero, respectively.
The x-intercept is the value of x that makes the numerator zero, so we set 3x-4 = 0 and solve for x. We get x = 4/3 as the x-intercept. This means the graph of f(x) crosses the x-axis at (4/3, 0).
The y-intercept is the value of y that makes the denominator zero, so we set f(x) = 0 and solve for y. We get y = f(0) = -4/15 as the y-intercept. This means the graph of f(x) crosses the y-axis at (0, -4/15).
To find the horizontal asymptote of the rational function f(x) = (3x-4) / (2x+3)(2x+5), we need to compare the degrees of the numerator and denominator. The degree of the numerator is 1, and the degree of the denominator is 2. Since the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at y = 0. This means that as x approaches positive or negative infinity, f(x) approaches zero.
Explanation: