Question

Which of the following Functions is NOT Linear? A:f(x)=x+0.5 B:F(x)=-x+0.5 C: F(x)=x^2-0.5 D: f(x)=0.5x

Answer 1

C: f(x) = x² - 0.5

Explanation:

The grsaph of the linear function is a straight line.

The equation of a line in the slope-intercept fomr is:

y = mx + b

where

m - slope

b - y-intercept

We have:

A: f(x) = x + 0.5

it's a linear function: m = 1, b = 0.5

B: f(x) = -x + 0.5

it's a linear function: m = -1, b = 0.5

C: f(x) = x² - 0.5

it's not a linear function because in the equation is square of x (x²).

The graph of this function is a parabola.

D: f(x) = 0.5x

it's a linear function: m = 0.5, b = 0

Answer 2

C: F(x)=x^2-0.5

Explanation:

When the x is squared it's a parabola. A linear graph is shaped like a straight line, while a parabola is curved inward. I have included a graph of what that function would look like (tap/click on it to see the full graph.)