Question

the table of values represents a continuous function.

x	-3	-1	1	3	5	7	9
g(x)	0.375	0.75	1.5	3	6	12	24

which type of function describes g(x)?

• exponential
• logarithmic
• polynomial
• rational

Explanation:

Step1: Check the ratio between consecutive g(x) values

Calculate the ratio of each \( g(x) \) value to the previous one:
\( \frac{0.75}{0.375} = 2 \), \( \frac{1.5}{0.75} = 2 \), \( \frac{3}{1.5} = 2 \), \( \frac{6}{3} = 2 \), \( \frac{12}{6} = 2 \), \( \frac{24}{12} = 2 \).

Step2: Analyze the function type

For an exponential function \( y = ab^x \), the ratio between consecutive \( y \)-values (when \( x \) increases by a constant amount) is constant (\( b \)). Here, the \( x \)-values increase by 2 each time (from -3 to -1, -1 to 1, etc.), and the ratio of \( g(x) \) values is always 2 (constant). Logarithmic, polynomial, and rational functions do not have a constant ratio between consecutive outputs for constant \( x \)-increments.

Answer:

Exponential