Given the function f(x)=-x-(4)/(5)x^(2), then what is f(x-3) as a simplified polynomial? Answer:

Understand function transformation: Understand the function transformation. We need to find f(x-3), which means we will replace every instance of x in the function f(x) with (x-3).Apply transformation to function: Apply the transformation to the function. f(x) = -x - (4/5)x^2 f(x-3) = -(x-3) - (4/5)(x-3)^2Expand terms in transformed function: Expand the terms in the transformed function. f(x-3) = -(x-3) - (4/5)(x^2 - 6x + 9)Distribute negative sign and fraction: Distribute the negative sign and the fraction across the terms. f(x-3) = -x + 3 - (4/5)x^2 + (24/5)x - (36/5)Combine like terms: Combine like terms, if any, to simplify the polynomial. There are no like terms to combine, so the polynomial is already in its simplest form.

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Given the function
f(x)=-x-(4)/(5)x^(2), then what is
f(x-3) as a simplified polynomial?
Answer:

Given the function $f(x)=-x-\frac{4}{5} x^{2}$ , then what is $f(x-3)$ as a simplified polynomial? $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find an equation

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Q. Given the function

f(x)=-x-\frac{4}{5} x^{2}

, then what is

f(x-3)

as a simplified polynomial?

\newline

Answer:

Understand function transformation: Understand the function transformation. $\newline$ We need to find $f(x-3)$ , which means we will replace every instance of $x$ in the function $f(x)$ with $(x-3)$ .
Apply transformation to function: Apply the transformation to the function. $\newline$ $f(x) = -x - \frac{4}{5}x^2$ $\newline$ $f(x-3) = -(x-3) - \frac{4}{5}(x-3)^2$
Expand terms in transformed function: Expand the terms in the transformed function. $f(x-3) = -(x-3) - \left(\frac{4}{5}\right)(x^2 - 6x + 9)$
Distribute negative sign and fraction: Distribute the negative sign and the fraction across the terms. $\newline$ $f(x-3) = -x + 3 - \frac{4}{5}x^2 + \frac{24}{5}x - \frac{36}{5}$
Combine like terms: Combine like terms, if any, to simplify the polynomial. $\newline$ There are no like terms to combine, so the polynomial is already in its simplest form.