Question

Which representations display nonlinear functions? Check all that apply.

On a coordinate plane, a line with negative slope goes through points (0, 1.5) and (2, 1).
On a coordinate plane, a parabola opens up.
A 2-column table with 4 rows. Column 1 is labeled x with entries 20, 21, 22, 23. Column 2 is labeled y with entries negative 1, negative 1.5, negative 2, negative 2.5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 12, negative 11, negative 10, negative 9. Column 2 is labeled y with entries 7, 11, 14, 17.

Answer 1

Nonlinear:
- The parabola that opens up (quadratic) — nonlinear.
- The table with x = −12, −11, −10, −9 and y = 7, 11, 14, 17 — nonlinear (y-changes are 4, 3, 3, not a constant rate).

Not nonlinear (linear):
- The line through (0, 1.5) and (2, 1) — straight line (constant slope).
- The table x = 20, 21, 22, 23 with y = −1, −1.5, −2, −2.5 — constant change in y (−0.5), so linear.