Question

Question content area top
Part 1
Graph the function.
​f(x)equalsStartFraction 3 Over x plus 2 EndFraction
Question content area bottom
Part 1
A.
-10
10
-10
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A graph has two branches. The first branch is below y equals negative 2 and to the left of the y-axis, approaching both. The second branch is above the y equals negative 2 and to the right of the y-axis, approaching both.
B.
-10
10
-10
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A graph has two branches. The first branch is below y equals 2 and to the left of the y-axis, approaching both. The second branch is above the y equals 2 and to the right of the y-axis, approaching both.
C.
-10
10
-10
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A graph has two branches. The first branch is below the x-axis and to the left of x equals negative 2, approaching both. The second branch is above the x-axis and to the right of the x equals negative 2, approaching both.
D.
-10
10
-10
10
x
y

Answer 1

C

Reason: f(x) = 3/(x+2) has a vertical asymptote x = −2 and a horizontal asymptote y = 0. For x < −2, f(x) < 0 so the left branch is below the x‑axis and approaches x = −2 and y = 0. For x > −2, f(x) > 0 so the right branch is above the x‑axis and approaches x = −2 and y = 0.