CPM Homework Help : PCT Problem 6-127

Graph $y=\frac { 2 x + 7 } { x - 7 }$ .

Hint:

Remember, fraction can’t have 0 in the denominator. Rewrite the function as a stretch and shift of $y=\frac{1}{x}$ .

What is the domain?

Check Graph (a):

Decreasing rational function, asymptotes are dashed lines at x = 7 & y = 2, left curve below & left of asymptote intersection, right curve above & right of asymptote intersection.

For each of the following questions, write the corresponding limit statement and evaluate it.
1. What happens to $y$ as $x$ gets close to $7$ and $x \gt 7$ ?
2. What happens to $y$ as $x$ gets close to $7$ and $x \lt 7$ ?
3. What happens to $y$ as $x$ approaches positive infinity?
4. What happens to $y$ as $x$ approaches negative infinity?