f(x) = x²(x – 1)³(x + 2)Determine end behavior of f (x). Explain reasons. Don't use a calculator.Find the zeros of f(x). State whether the graph crosses the x-axis, or touches the x-axis andturns around at each intercept.Find the y-intercept.Does the graph has y-axis symmetry, origin symmetry, or neither?

Answered: f(x) = x²(x – 1)³(x + 2) Determine end…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

f(x) = x²(x – 1)³(x + 2)
Determine end behavior of f (x). Explain reasons. Don't use a calculator.
Find the zeros of f(x). State whether the graph crosses the x-axis, or touches the x-axis and
turns around at each intercept.
Find the y-intercept.
Does the graph has y-axis symmetry, origin symmetry, or neither?

Expert Solution

Step 1

An algebraic expression is obtained by combining numbers and variables together with arithmetic operators.

If an expression contains only one term then it is called a monomial. Similarly and algebraic expression with 2 or 3 terms is called binomial and trinomial respectively.

And if an expression contains two or more terms then it is called a polynomial.

An algebraic expression of the form $a + b x + c x^{2} + d x^{3} + \cdot \cdot \cdot$ is called a polynomial in one variable. Here, x is the variable and a, b, c, and d are constants.