1.6.A.1Concept
As input values of a nonconstant polynomial function increase without bound, the output values will either increase or decrease without bound. The corresponding mathematical notation is limx→∞ p(x) = ∞ or limx→∞ p(x) = −∞.
ExampleOutputs rise without bound1 / 4
Let p(x) = x³ − 4x. Describe what happens to p(x) as x increases without bound, and write it with limit notation.
| x | 10 | 100 | 1,000 |
| p(x) | 960 | 999,600 | 999,996,000 |
Try it on paper first, then reveal each step to check your work.
Step 1 — Compute large inputs
p(10) = 1,000 − 40 = 960. p(100) = 1,000,000 − 400 = 999,600. p(1000) = 1,000,000,000 − 4,000 = 999,996,000.