which equation represents a nonlinear function?\na ( y = 5x - 3 )\nb ( y=\frac{x}{6}+2 )\nc ( y = x^{2}-4…
which equation represents a nonlinear function?\na ( y = 5x - 3 )\nb ( y=\frac{x}{6}+2 )\nc ( y = x^{2}-4 )\nd ( y=\frac{3}{5}x + 2 )
Answer
Explanation:
Step1: Recall the form of a linear function
A linear function has the form (y = mx + b), where (m) is the slope and (b) is the y - intercept, and the highest power of (x) is (1).
Step2: Analyze each option
- Option A: (y = 5x-3) is in the form (y = mx + b) ((m = 5), (b=-3)), so it is linear.
- Option B: (y=\frac{x}{6}+2=\frac{1}{6}x + 2) is in the form (y = mx + b) ((m=\frac{1}{6}), (b = 2)), so it is linear.
- Option C: (y=x^{2}-4) has the highest power of (x) equal to (2). A function of the form (y = ax^{2}+bx + c) ((a\neq0)) is a quadratic (non - linear) function.
- Option D: (y=\frac{3}{5}x+2) is in the form (y = mx + b) ((m=\frac{3}{5}), (b = 2)), so it is linear.
Answer:
C. (y = x^{2}-4)