Question

Consider f(x) = bx. which statement(s) are true for 0 < b < 1? check all that apply. the domain is all real numbers. the domain is x > 0. the range is all real numbers. the range is y > 0. the graph has x-intercept 1. the graph has a y-intercept of 1. the function is always increasing. the function is always decreasing.

Answer 1

The true statement for f(x)=b^x is the function is always decreasing function.

We have given,

f(x)=b^x where 0<b<1

What is the domain?

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

We can select any values of x for which function

It will be defined for all real x

So, the domain is $(-\infty,\infty)$

The range is all possible values of y for which x is defined

we are given that b is positive

The value of the function will always be positive

So, the range is  $(0,\infty)$

y>0

The x-intercept:

Set f(x)=0 and then we can solve for x

f(x)=b^x=0

x is undefined

The x-intercept does not exist

Increasing or decreasing:

Since, 0<b<1

The b is a positive value less than 1

As we increase the value of, $b^x$ will keep decreasing

This is decreasing function

To learn more about the function visit:

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