How to determine between which consecutive integers the real zeros

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Approximate Zeros A. Determine between which consecutive integers the real zeros of are located on the interval [– 2, 2]. Investigate function values on the interval [-2, 2].

Approximate Zeros Because f (-1) is positive and f (0) is negative, by the Location Principle, f (x) has a zero between -1 and 0. The value of f (x) also changes sign for [1, 2]. This indicates the existence of real zeros in each of these intervals. The graph of f (x) supports this conclusion. Answer: There are two zeros on the interval, – 1 < x < 0 and 1 < x < 2.

Approximate Zeros B. Determine between which consecutive integers the real zeros of f (x) = x 3 + 2 x + 5 are located on the interval [– 2, 2]. Investigate function values on the interval [– 2, 2].

Approximate Zeros Because f (-2) is negative and f (– 1) is positive, by the Location Principle, f (x) has a zero between – 2 and – 1. This indicates the existence of a real zero on this interval. The graph of f (x) supports this conclusion. – 3 Answer: – 2 < x < – 1. 1 1 3

A. Determine between which consecutive integers the real zeros of f (x) = x 3 + 2 x 2 – x – 1 are located on the interval [– 4, 4]. A. – 1 < x < 0 B. – 3 < x < – 2 and – 1 < x < 0 C. – 3 < x < – 2 and 0 < x < 1 D. – 3 < x < – 2, – 1 < x < 0, and 0 < x < 1

B. Determine between which consecutive integers the real zeros of f (x) = 3 x 3 – 2 x 2 + 3 are located on the interval [– 2, 2]. A. – 2 < x < – 1 B. – 1 < x < 0 C. 0 < x < 1 D. 1 < x < 2

Graphs that Approach Infinity Use the graph of f(x) = x 3 – x 2 – 4 x + 4 to describe its end behavior. Support the conjecture numerically.