Select the correct answer. Exponential function f is represented by the table. x & -2 & -1 & 0 & 1 & 2 f(x) & -62 & -30 & -14 & -6 & -2 Function g is represented by the equation. [ g(x)=-20((1)/(2))^x+10 ] Which statement correctly compares the two functions on the interval [-2,1] ? A. Both functions are increasing, but function g increases at a faster average ra B. Only function f is increasing, and both functions are negative. C. Both functions are increasing, but function f increases at a faster average rate D. Only function f is increasing, and only function f is negative.

## Step 1: Analyze Function ### The function \( f(x) \) is represented by the table. We observe the values of \( f(x) \) for . The values are , respectively. As increases from to , \( f(x) \) also increases, indicating that \( f(x) \) is an increasing function on the interval .## Step 2: Analyze Function ### The function \( g(x) = -20\left(\frac{1}{2}\right)^{x} + 10 \) is given. We need to evaluate this function at :- For : - For : - For : - For : ### From these calculations, we see that \( g(x) \) is also increasing on the interval .## Step 3: Compare the Functions### Both functions and are increasing on the interval . However, we need to compare their average rates of increase. The average rate of increase for a function over an interval can be calculated as the change in function value divided by the change in .- For \( f(x) \) from to : - For \( g(x) \) from to : ### Comparing the average rates, \( g(x) \) increases at a faster average rate than \( f(x) \).