which are true of the function ( f(x)=49left(\frac{1}{7}\right)^{x} )? select three options. the domain is…

which are true of the function ( f(x)=49left(\frac{1}{7}\right)^{x} )? select three options. the domain is the set of all real numbers. the range is the set of all real numbers. the domain is ( x>0 ). the range is ( y>0 ). as ( x ) increases by 1, each ( y )-value is one - seventh of the previous ( y )-value.

which are true of the function ( f(x)=49left(\frac{1}{7}\right)^{x} )? select three options. the domain is the set of all real numbers. the range is the set of all real numbers. the domain is ( x>0 ). the range is ( y>0 ). as ( x ) increases by 1, each ( y )-value is one - seventh of the previous ( y )-value.

Answer

Explanation:

Step1: Analyze the domain of an exponential function

For an exponential function (y = a\cdot b^{x}), (x) can be any real number. So for (f(x)=49(\frac{1}{7})^{x}), the domain is the set of all real numbers.

Step2: Analyze the range of an exponential function

Since (a = 49>0) and (b=\frac{1}{7}), and (b^{x}>0) for all real (x), then (y = 49(\frac{1}{7})^{x}>0). So the range is (y > 0).

Step3: Analyze the relationship between consecutive (y)-values

Let (x_{1}) and (x_{2}=x_{1}+ 1). Then (y_{1}=49(\frac{1}{7})^{x_{1}}) and (y_{2}=49(\frac{1}{7})^{x_{1}+1}=49(\frac{1}{7})^{x_{1}}\cdot\frac{1}{7}=\frac{1}{7}y_{1}). So as (x) increases by 1, each (y)-value is one - seventh of the previous (y)-value.

Answer:

The domain is the set of all real numbers, The range is (y>0), As (x) increases by 1, each (y)-value is one - seventh of the previous (y)-value.