Answer:
a) f(x) = x²
As x→[infinity], f(x)→[infinity]
As x→−[infinity], f(x)→[infinity]
For this function, f(x) increases without bound as the input increases or decreases without bound. The graph of this function would be symmetric about the y-axis.
b) g(x) = x³
As x→[infinity], g(x)→[infinity]
As x→−[infinity], g(x)→-[infinity]
g(x) increases without bound as the input x increases without bound and decreases also without bound as input x decreases without bound. The graph of this function would be symmetric about the origin.
c) h(x)=−6x³.
As x→[infinity], h(x)→-[infinity]
As x→−[infinity], h(x)→[infinity]
h(x) decreases without bound as the input x increases without bound and increases without bound as input x decreases without bound. The graph of this function would also be symmetric about the origin.
Explanation:
Normally, end behaviours predict the nature of the graphs of functions (especially as the values of x become very large, both in the positive and negative sense.
f(x) = x²
As x →[infinity],
f(x) = (∞)² → ∞
f(x) →[infinity]
And as x →−[infinity],
f(x) = (-∞)² → ∞
f(x) →[infinity]
For this function, f(x) increases without bound as the input increases or decreases without bound. The graph of this function would be symmetric about the y-axis.
b) g(x) = x³
As x→[infinity],
g(x) = (∞)³ → ∞
g(x)→[infinity]
As x→−[infinity],
g(x) = (-∞)³ → -∞
g(x)→−[infinity]
g(x) increases without bound as the input x increases without bound and decreases also without bound as input x decreases without bound. The graph of this function would be symmetric about the origin.
c) h(x)=−6x³.
As x→[infinity],
h(x) = -6(∞)³ → -6(∞) → -∞
h(x)→-infinity]
As x→−[infinity],
h(x) = -6(-∞)³ → -6(-∞) → ∞
h(x)→[infinity]
h(x) decreases without bound as the input x increases without bound and increases without bound as input x decreases without bound. The graph of this function would also be symmetric about the origin.
Hope this Helps!!!