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Which equations define $y$ as a nonlinear function of $x$ ? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $y = \frac{3x}{2}$ $\newline$ (B) $y - 4 = 3x^2$ $\newline$ (C) $y = x^5 + 6$ $\newline$ (D) $2y = 12$ $\newline$ (E) $y = 7x - x$ $\newline$ (F) $y = 7x \times x$

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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 = \frac{3x}{2}

\newline

(B)

y - 4 = 3x^2

\newline

(C)

y = x^5 + 6

\newline

(D)

2y = 12

\newline

(E)

y = 7x - x

\newline

(F)

y = 7x \times x

Identify Linearity: Identify if the function $y = \frac{3x}{2}$ is nonlinear. $\newline$ Calculation: $y = \frac{3x}{2}$ is a linear function because it can be rewritten as $y = \left(\frac{3}{2}\right)x$ , which is in the form $y = mx + b$ .
Check Quadratic Function: Check if the equation $y - 4 = 3x^2$ defines $y$ as a nonlinear function. $\newline$ Calculation: Rearrange to $y = 3x^2 + 4$ . This is a quadratic function, which is nonlinear.
Examine Polynomial Degree: Examine if $y = x^5 + 6$ is nonlinear. $\newline$ Calculation: $y = x^5 + 6$ represents a polynomial of degree $5$ , which is nonlinear.
Analyze Constant Function: Analyze if $2y = 12$ defines $y$ as a nonlinear function. $\newline$ Calculation: Simplify to $y = 6$ . This is a constant function, which is linear.
Determine Linear Equation: Determine if $y = 7x - x$ is nonlinear. $\newline$ Calculation: Simplify to $y = 6x$ . This is a linear function, as it can be expressed in the form $y = mx + b$ .
Assess Quadratic Function: Assess if $y = 7x \times x$ defines $y$ as a nonlinear function. $\newline$ Calculation: Rewrite as $y = 7x^2$ . This is a quadratic function, which is nonlinear.

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