Question

Graph the function.
​f(x)equalsStartFraction 10 Over x squared EndFraction
minus1
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. From left to right, the first branch rises shallowly in quadrant three, passes through (negative 3.2, 0), then rises steeply in quadrant 2. As x decreases towards negative infinity, the curve approaches y = negative 1 from above. From left to right, the second branch falls steeply in quadrant 1, passes through (3.2, 0), then falls shallowly in quadrant 4. As x increases towards infinity, the curve approaches y = negative 1 from above. All coordinates are approximate.
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. From left to right, the first branch falls shallowly in quadrant three, then falls steeply. As x decreases towards negative infinity, the curve approaches y = negative 1 from below. From left to right, the second branch falls steeply in quadrant 1 passing through (5, 0), then falls shallowly. As x increases towards infinity, the curve approaches y = negative 1 from above. All coordinates are approximate.
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. From left to right, the first branch rises shallowly in quadrant three, passes through (negative 3.2, 2), then rises steeply, approaching the y-axis from the left. As x decreases towards negative infinity, the curve approaches y = 1 from above. From left to right, the second branch falls steeply in quadrant 1, passes through (3.2, 2), then falls shallowly. As x increases towards infinity, the curve approaches y = 1 from above. All coordinates are approximate.
D.
-10
10
-10
10
x
y

Answer 1

A.

Reason: f(x) = 10/x^2 − 1 is even (symmetric about the y‑axis), has a vertical asymptote at x = 0 (f → +∞ as x → 0±), and a horizontal asymptote y = −1 (10/x^2 > 0 so f → −1 from above as |x| → ∞). The x‑intercepts satisfy 10/x^2 − 1 = 0 → x = ±√10 ≈ ±3.16, so each branch crosses the x‑axis near ±3.2 and has the described quadrant behavior.