Let $$ f(x)=\frac{5}{7 x+2} $$ This function has: 1) A horizontal asymptote at $$ y=\square $$ 2) A vertical asymptote at $$ x=\square $$

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To find the asymptotes of the function $$ f(x) = \frac{5}{7x + 2} $$, we can analyze the function as follows:

1) **Horizontal Asymptote**: 
   The horizontal asymptote of a rational function is determined by the degrees of the polynomial in the numerator and the denominator. In this case, the numerator is a constant (degree 0) and the denominator is a linear function (degree 1).

As $$ x $$ approaches infinity (or negative infinity), the value of $$ f(x) $$ approaches 0 because the denominator grows much larger than the constant numerator. Therefore, the horizontal asymptote is:
   $$
   y = 0
   $$

2) **Vertical Asymptote**: 
   The vertical asymptote occurs where the denominator is equal to zero (and the numerator is not zero). We set the denominator equal to zero and solve for $$ x $$:
   $$
   7x + 2 = 0
   $$
   $$
   7x = -2
   $$
   $$
   x = -\frac{2}{7}
   $$
   Thus, the vertical asymptote is at:
   $$
   x = -\frac{2}{7}
   $$

In summary, the function $$ f(x) = \frac{5}{7x + 2} $$ has:
1) A horizontal asymptote at $$ y = 0 $$
2) A vertical asymptote at $$ x = -\frac{2}{7} $$
1) A horizontal asymptote at $$ y = 0 $$ 2) A vertical asymptote at $$ x = -\frac{2}{7} $$

Let
This function has:

A horizontal asymptote at

A vertical asymptote at

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