Question

Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-1, 2]? A. Both functions are increasing, but function f increases at a faster average rate. B. Only function f is increasing, but both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Only function f is increasing, and only function f is negative.

Answer 1

Both functions are increasing, but function g increases at a faster average rate.

The correct option is (C)

What is an increasing function?

If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.

let f(x) = $ab^{x} +c$ and x=0 , f(0)= -10

-10=a+c

Now,

f(x) = -33/5*$(\frac{1}{11} )^{x}$ - 17/5

f '(x)>0

So, x is increasing function.

g(x) = -18/3*$(\frac{1}{11} )^{x}$ +2

g'(x) =-18$(\frac{1}{3} )^{x}$ln(1/3)

ln 1/3<0

So, g'(x)>0

So, g(x) is an increasing function.

For any x ∈ f(x) and x ∈ g(x)

Since, g increases at a faster rate.

Hence, Both functions are increasing, but function g increases at a faster.

Learn more about increasing function here:

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