Question

How do I find out if a function is logarithmic, exponential, or quadratic by only looking at a table?

Answer 1

To determine if a function is logarithmic, exponential, or quadratic by looking at a table, you can examine the patterns in the values of the function as the input increases.

Step-by-step explanation:

By looking at a table, you can determine if a function is logarithmic, exponential, or quadratic by examining the patterns in the values of the function as the input increases. Here are some key indicators:

Logarithmic:

1. If the ratio of consecutive outputs is constant, the function is logarithmic. For example, if the ratio of f(x+1) to f(x) is always the same, then the function is logarithmic.
2. If the outputs increase by smaller increments as the input increases, the function is logarithmic. For example, if f(x+1) - f(x) is always smaller than f(x+2) - f(x+1), then the function is logarithmic.

Exponential:

1. If the ratio of consecutive outputs is increasing or decreasing exponentially, the function is exponential. For example, if the ratio of f(x+1) to f(x) increases or decreases at a constant rate, then the function is exponential.
2. If the outputs increase by larger increments as the input increases, the function is exponential. For example, if f(x+1) - f(x) is always larger than f(x+2) - f(x+1), then the function is exponential.

Quadratic:

1. If the outputs increase by a constant difference as the input increases, the function is quadratic. For example, if f(x+1) - f(x) is always the same, then the function is quadratic.
2. If the ratio of consecutive outputs is increasing or decreasing at a constant rate, the function may be quadratic. For example, if the ratio of f(x+1) to f(x) increases or decreases at a constant rate, the function may be quadratic.