Question

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

Answer 1

Answer:

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Consider f(x) = $b^{x}$. 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.

My answer:

The domain is all real numbers.

True, the domain of a function is the complete set of possible values of the independent variable. Here, we can have unlimited values of x so we will have unlimited values of f(x)

<=> our domain (0 , +∞ )

The domain is x > 0.

Wrong, as we discussed in the aforementioned answer.

The range is all real numbers.

Wrong

The range is y > 0.

True, the range of a function is the complete set of all possible resulting values of the dependent variable (f(x), usually), after we have substituted the domain. Because this is an exponential function so:

<=> our range  (0 , +∞ )  or y>0

The graph has x-intercept 1.

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

The graph has a y-intercept of 1

y-intercept when x is 0, so f(x) = 1 . True.

The function is always decreasing

Because 0 < b < 1, The function is always decreasing when we increase the value of x.

So we choose A D F H