Question

which table represents a linear function?
x | f(x)
1 | 1
4 | 2
9 | 3

Explanation:

Step1: Recall linear function property

A linear function has a constant rate of change, meaning the slope between any two points \((x_1, f(x_1))\) and \((x_2, f(x_2))\) is constant. The slope formula is \(m=\frac{f(x_2)-f(x_1)}{x_2 - x_1}\).

Step2: Analyze the first table

For the first table:

• Between \((1, 1)\) and \((4, 2)\): \(m_1=\frac{2 - 1}{4 - 1}=\frac{1}{3}\)
• Between \((4, 2)\) and \((9, 3)\): \(m_2=\frac{3 - 2}{9 - 4}=\frac{1}{5}\)

Since \(m_1
eq m_2\), this table does not represent a linear function. (Assuming the other table, not fully shown, has a constant slope. For example, if another table has \(x\) values with equal differences and \(f(x)\) values with equal differences, like \(x: 1, 2, 3\) and \(f(x): 2, 4, 6\), slope is \(2\) everywhere.)

Answer:

(Assuming the other table (not fully shown) with constant slope, e.g., if options are A (first table) and B (other), then B. But since the other table is not fully visible, but based on the first table's non - linearity, the correct table is the one with constant slope, likely the other option not shown here in full but with consistent differences.)