ooo TMobile LTE 244 PM 87 coursesapexlearningcom nential and

ooo T-Mobile LTE 2:44 PM 87% courses.apexlearning.com nential and Logarithmic Functions SUBMIT Question 21 of 25 Multiple Choice: Please select the best answer and click \"submit.\" What are the domain and range of the exponential function below? F(x) = 5x + 6 0 A. Domain: All real numbers greater than 0 Range: All real numbers greater than 6 O B. Domain: All real numbers greater than 0 Range: All real numbers greater than 0 O C. Domain: All real numbers Range: All real numbers greater than 0 D. Domain: All real numbers Range: All real numbers greater than 6

Solution

Given

f(x) = 5^x +6

Domain means all possible values that \"x\" can take so that f(x) is real.

Range means all possible values of \"y\"

Domain       ->   f(x) = 5^x + 6             

                 we can plug any value for \"x\" here.                 

// lets plug x = 1 we get   f(x) = 5¹ + 6 => 5+6 => 11        (real)

lets plug x =0 we get    f(x) = 5⁰ + 6 => 1+6 => 7         (real)

x= -1 we get f(x) = 5^-1 + 6 => 1/5+6 => 6.2       (real)

since we can plug any value for \"x\" therefore domain is all real number

Range

f(x) = 5^x + 6   // 5^x plugging any value for \"x\" will be greater then zero and \"+6\" so the range will be greater then \"6\".

lets plug x = 1 we get   f(x) = 5¹ + 6 => 5+6 => 11       

lets plug x =0 we get    f(x) = 5⁰ + 6 => 1+6 => 7        

x= -1 we get f(x) = 5^-1 + 6 => 1/5+6 => 6.2   

we can see that we plugging any value for \"x\" we get f(x) > 6  

option (d)