Question

Algebra 2 please help

Answer 1

For what values of b is f(x) = b^x an increasing function?

Answer 2

A. Any real number
B. b > 0
C. b > 1
D. 0< b <1

Answer 3

@pgpilot326

Answer 4

@shamil98

Answer 5

these are exponentials and b>0 (otherwise if b<0 it's a complex valued function). So you can ignore the first choice.

you should see that one of them works and the others don't. try a couple...

start with a simple one... say the last

is it increasing?

Answer 6

yes

Answer 7

let's look...

0<1/2<1/

(1/2)^1 = 1/2
(1/2)^2 = 1/4

so as x increases, f(x) decreases... not an increasing function.

Answer 8

so it would be D right

Answer 9

what if b = 1. then

1^1 = 1
and 1^2 = 1

so b = 1 is neither increasing nor decreasing.

(it's the same for all of these if you use negative exponents, or fractional exponents or real exponents... so long as the exponents are increasing)

Answer 10

no. D is not right.

Answer 11

because at first i thought it was B but then you said is neither increasing nor decreasing so yeah

Answer 12

look at the values in those intervals... it would have to be true for all values of b in the interval.

the only one that works is C.

Answer 13

D is strictly decreasing.
C is strictly increasing
B is increasing, decreasing and neither depending on the value
(0<b<1 it's decreasing, b>1 it's increasing, b = 1 it's neither)

for A, it's increasing, decreasing, neither and a complex valued function depending on the value of b.
(0<b<1 it's decreasing, b>1 it's increasing, b = 1 or 0 it's neither, if b<0 it's a complex valued function)

Answer 14

did i help you?

Answer 15

yes a lot thank you very much if i could give you more medals i would because you really did help thank you so much :) <3

Answer 16

you're welcome