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

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Domain and range of quadratic functions: equations

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^4 + 5

\newline

(B)

y = \frac{x}{4}

\newline

(C)

y = x + 2^2

\newline

(D)

4y = 3x

\newline

(E)

y = 5x^2

\newline

(F)

y = 3 - 5x

Identify function type: Step $1$ : Identify the type of each function. $\newline$ - (A) $y = 4x^4 + 5$ involves $x$ raised to the fourth power, which is a polynomial of degree $4$ , hence nonlinear.
Select nonlinear equations: Step $2$ : Select all equations that are nonlinear. $\newline$ - From Step $1$ , the nonlinear functions are given by equations $(A)$ and $(E)$ .

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