The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.

Given the table

x f(x)

-2 -46

-1 -22

0 -10

1 -4

2 -1

We have to choose which statement describes better about function

Let us assume $f(x)=ab^x+c$

at x=0, f(0)=-10

So, -10 =a+c

Similarly, by satisfying the above table in the f(x)

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

$f'(x) > 0$

So we can say that f(x) is an increasing function.

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

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

ln(1/3) < 0

So, g^ \prime (x) > 0

So, g(x) is an increasing function.

For any x∈f(x) and x∈g(x) $g'(x) > f'(x)$

So, g increases at a faster average rate

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

Learn more about increasing functions here: brainly.com/question/12940982

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7 0

1 year ago

How do I describe the real zeroes of this function using Descartes's Rule of Signs?

Serhud [2]

The number of positive roots is the number of changes of signs there are, then decrease by 2 each time and stop when you get to 1 or 0

negative roots, sub every x with -x and reevaluate, count change of signs
decrease by 2 each time and stop when you get to 1 or 0

y=+2x⁵-x⁴-2x³+4x²+x-2
+,-,-,+,+,-
1 2 3

3 or 1 positive roots

replace x with -x ( baically flip all signs of odd powerd numbers)

y=-2x⁵-x⁴+2x³+4x²-x-2
-,-,+,+,-,-
1 2

2 or 0 negative roots

3 or 1 positive roots
2 or 0 negative roots
2nd option is answer

4 0

3 years ago