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Which equations define $y$ as a nonlinear function of $x$ ? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $y = 4x^2 + 5x - 8$ $\newline$ (B) $y = -8 + 5x$ $\newline$ (C) $y = x^3 + 1$ $\newline$ (D) $y = x - 9^2$ $\newline$ (E) $y = \sqrt{x} - 3$ $\newline$ (F) $y = x^2$

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Find derivatives of using multiple formulae

Full solution

Q. Which equations define

y

as a nonlinear function of

x

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

y = 4x^2 + 5x - 8

\newline

(B)

y = -8 + 5x

\newline

(C)

y = x^3 + 1

\newline

(D)

y = x - 9^2

\newline

(E)

y = \sqrt{x} - 3

\newline

(F)

y = x^2

Analyze Equation (A): Step $1$ : Analyze equation (A) $y = 4x^2 + 5x - 8$ . Nonlinear functions include terms with exponents greater than $1$ . Here, $x^2$ is present.
Analyze Equation (B): Step $2$ : Analyze equation (B) $y = -8 + 5x$ . This is a linear equation because it can be rewritten as $y = 5x - 8$ , which is in the form $y = mx + b$ .
Analyze Equation (C): Step $3$ : Analyze equation (C) $y = x^3 + 1$ . The term $x^3$ makes this a nonlinear function, as the exponent is greater than $1$ .
Analyze Equation (D): Step $4$ : Analyze equation (D) $y = x - 9^2$ . This simplifies to $y = x - 81$ , which is linear ( $y = x + b$ ).
Analyze Equation (E): Step $5$ : Analyze equation (E) $y = \sqrt{x} - 3$ . The square root function is nonlinear.
Analyze Equation (F): Step $6$ : Analyze equation (F) $y = x^2$ . This is clearly a nonlinear function due to the $x^2$ term.

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