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

Identify Linearity: Identify if the function y = 3x/2 is nonlinear. Calculation: y = 3x/2 is a linear function because it can be rewritten as y = (3/2)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. 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. 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. Calculation: Simplify to y = 6. This is a constant function, which is linear.Determine Linear Equation: Determine if y = 7x - x is nonlinear. 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 * x defines y as a nonlinear function. Calculation: Rewrite as y = 7x^2. This is a quadratic function, which is nonlinear.

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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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Math Problems

Algebra 2

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.