Question

mr. richardson, math 2 (1h1.9). convert factored form to standard form, 10/7/25
name: jonathan francis period 2

1. x f(x)

0 -1
1 -1/2
2 0
3 1/2
4 1
what type of function is represented in the table above:

Explanation:

Step1: Check for constant - rate of change

Find the differences in \(y\) - values (\(f(x)\)) and \(x\) - values. The change in \(x\) is \(\Delta x=1\) for each step (\(1 - 0=1\), \(2 - 1 = 1\), etc.). The change in \(y\) is \(\Delta y=-\frac{1}{2}-(-1)=\frac{1}{2}\), \(0-(-\frac{1}{2})=\frac{1}{2}\), \(\frac{1}{2}-0=\frac{1}{2}\), \(1 - \frac{1}{2}=\frac{1}{2}\). Since the rate of change \(\frac{\Delta y}{\Delta x}=\frac{1}{2}\) is constant.

Step2: Recall function types

A linear function has a constant rate of change. A quadratic function has a non - constant rate of change of the first - difference. An exponential function has a constant ratio between consecutive \(y\) - values. Since the rate of change between consecutive \(y\) - values for a constant change in \(x\) is constant, it is a linear function.

Answer:

Linear function