Question

studying for my test and not sure how to do these kinds of problems. Please help.
select the function whose graph is decreasing and whose range is (0,∞).
1. y=b^x, b<1
2. y=b^x, b>1
3. y=log(base b)x, b<1
4. y=log(base b)x, b>1

Answer 1

y= b^x and b<1
y'= b^x \ln b <0 so y s decreasing from Infinity to zero

Answer 2

thank you, but I'm not really sure how you got it. I struggle with graphing.

Answer 3

\[
\ln(b) < 0
\]
since b<1
and b^x is always positive. Their product is negative. So the function is decreasing.

Answer 4

The first number is correct answer because if you will take a number less than 1 if you will increase the power number will be decreased for if we will
take .5 as the base and we are giving the power than it will be decreased
Let graph for you...

Answer 5

Consider only from 0 to infinity....

Answer 6

check it @jkd13

Answer 7

I'm looking at the graph now.

Answer 8

consider from 0 to infinity when will put zero output will be one and when we will increase power to one it will f(x)=.5 it means it is decreased form 1 to .5

Answer 9

Did you get it @jkd13

Answer 10

still not too confident about it but i have a better idea so ill look over my book some more and look at a few examples and i should get it! thank you for your help!

Answer 11

suppose we have a function
f(x)=.5^x
now the domain is from 0 to infinity so start from zero and observe the outputs.
f(0)=.5^0=1
f(1)=.5^1=.5
f(2)=.5^2=.25

Answer 12

@jkd13

Answer 13

ok! yeah i get it. I'm still gonna look over a few to be on the safe side though! thank you!