Question

a function where the rate of change varies is called a
__________ function.

in a graph, a linear function forms a __________.

Explanation:

First Question:

A function with a varying rate of change means its slope (rate of change) isn't constant. Non - linear functions (like quadratic, exponential etc.) have rates of change that vary. For example, in a quadratic function \(y = x^{2}\), the derivative (rate of change) is \(y'=2x\), which changes as \(x\) changes. So the function with a varying rate of change is a non - linear function.

A linear function has the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. When we graph this function, the points \((x,y)\) that satisfy the equation lie on a straight line. This is a fundamental property of linear functions.

Answer:

non - linear

Second Question: