Question

Which of the following functions is not linear?

Answer 1

Answer:

D. y = 8x² + 8x + 4

Step-by-step explanation:

The equation of a linear function is in form:

$y=mx+b$

We have:

$\bold{A.}\\\\y=8(x+8)+4(x+8)\qquad\text{use the distributive property}\\\\y=8x+64+4x+32\qquad\text{combine like terms}\\\\y=12x+86\to m=12,\ b=86\\\\\bold{linear\ function}$

$\bold{B.}\\\\y=\dfrac{\sqrt8}{8}x-4\to m=\dfrac{\sqrt8}{8},\ b=-4\\\\\bold{linear\ function}$

$\bold{C.}\\\\y=\dfrac{1}{8}x+8\to m=\dfrac{1}{8},\ b=8\\\\\bold{linear\ function}$

$\bold{D.}\\\\y=8x^2+8x+4\\\\\bold{not\ linear\ function}\\\\\text{because is}\ x^2\\\\\text{It's a quadratic function}$