Question

Y – x² = 4.5 and y = x^4

Is this function linear or non linear?

Also show work and explain why.

Answer 1

Linear functions are in the form of y = mx + b.

y - x² = 4.5 is not linear because of the x².

y = x⁴ is not linear because of x⁴.

Answer 2

Linear functions are in the form y=mx+b.

But the functions are in the form of y=x^4 and y-x^2=4.5.
Their exponents make them a quadratic function so it doesn't have the same rate of change. Therefore the equations are not linear. They are quadratic.