Question

Graph the function.
​f(x)equalsStartFraction 10 Over x squared EndFraction
minus3
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Part 1
A.
-10
10
-10
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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 3 from below. From left to right, the second branch falls steeply in quadrant 1 passing through (1.7, 0), then falls shallowly. As x increases towards infinity, the curve approaches y = negative 3 from above. All coordinates are approximate.
B.
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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 1.8, 6), then rises steeply, approaching the y-axis from the left. As x decreases towards negative infinity, the curve approaches y = 3 from above. From left to right, the second branch falls steeply in quadrant 1, passes through (1.8, 6), then falls shallowly. As x increases towards infinity, the curve approaches y = 3 from above. All coordinates are approximate.
C.
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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 in quadrant three, passes through (negative 1.7, 0), then falls steeply in quadrant 3. As x decreases towards negative infinity, the curve approaches y = 3 from below. From left to right, the second branch falls steeply in quadrant 1, then falls shallowly. As x increases towards infinity, the curve approaches y = 3 from above. All coordinates are approximate.
D.
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Answer 1

D.

Reason: f(x) = 10/x^2 − 3 is even, has a vertical asymptote at x = 0 (10/x^2 → +∞ as x → 0±) and a horizontal asymptote y = −3 (10/x^2 → 0 so f → −3). Since 10/x^2 > 0 for x ≠ 0, f(x) > −3 for all x ≠ 0 so the graph approaches y = −3 from above. The x–intercepts satisfy 10/x^2 − 3 = 0 ⇒ x = ±√(10/3) ≈ ±1.826. The right branch: +∞ as x→0+, crosses at ≈(1.826,0) and decreases toward −3 as x→+∞; the left branch is symmetric. These features match choice D.