Question

Consider f(x) = bx. Which statement(s) are true for 0 < b < 1? Check all that apply:

Answer 1

Answer:

The Domain is all real numbers.

The range is y > 1.

The graph has a y-intercept of 1.

The function is always decreasing.

Step-by-step explanation:

Answer 2

we are given

$f(x)=b^x$

where 0<b<1

Domain:

domain is all possible values of x for which any function is defined

so, we can select any values of x for which function

it will be defined for all real x

so, domain is

$(-\infty,\infty)$

Range:

Range is all possible values of y for which x is defined

we are given that b is positive

so, value of function will always be positive

so, range is

$(0,\infty)$

or

y>0

x-intercept:

we can set f(x)=0

and then we can solve for x

$f(x)=b^x=0$

x is undefined

so, x-intercept does not exist

Increasing or decreasing:

Since, 0<b<1

so, b is positive value less than 1

so, as we increase value of , b^x will keep decreasing

so, this is decreasing