For each function, determine whether it is a polynomial function.Function Is the function a polynomial?Yes No=gx+−75x (a) =gx+−75x=fx+5x5−x386 (b) =fx+5x5−x386=hx−6x7x3 (c) =hx−6x7x3=vx8 (d) =vx8
Question
For each function, determine whether it is a polynomial function.Function Is the function a polynomial?Yes No=gx+−75x (a) =gx+−75x=fx+5x5−x386 (b) =fx+5x5−x386=hx−6x7x3 (c) =hx−6x7x3=vx8 (d) =vx8
Solution
(a) =gx+−75x: Yes, this is a polynomial function. Polynomial functions are composed of variables, exponents, and coefficients, and this function fits that description.
(b) =fx+5x5−x386: No, this is not a polynomial function. In a polynomial, the exponents of the variable must be non-negative integers. Here, the exponent 386 is not a non-negative integer.
(c) =hx−6x7x3: Yes, this is a polynomial function. All the exponents of the variable are non-negative integers.
(d) =vx8: Yes, this is a polynomial function. The exponent of the variable is a non-negative integer.
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