Question

if f(x)=2^x -10 and the domain of f(x) is the set of integers from -1 to 3, which values are elements of the range of f (x)? Select all that apply. a) -12 b)-10 c)-9 d)-6 e)-2

Answer 1

The domain of the function is the range of values of x that can be used to be replaced in the equation for it to become true. We are given that the value of f(x) should range only from -1 to 3. We evaluate each of the choices and see if the values of f(x) will fall within the range.

(a) -12;   f(x) = 2^(-12) - 10 = -9.9999 (NOT AN ANSWER)
(b) -10;   f(x) = 2^(-10) - 10 = -9.999 (NOT AN ANSWER)
(c) -9;     f(x) = 2^(-9) - 10 = -9.999 (NOT AN ANSWER)
(d) -6;     f(x) = 2^(-6) - 10 = -9.98 (NOT AN ANSWER) 
(e) -2;      f(x) = 2^(-2) - 10 = -9.75 (NOT AN ANSWER)

Hence, none of the choices will allow the value of f(x) to fall between -1 and 3. 

Answer 2

The range is all number greater than -10, so the values that are elements of the range of f(x) are c) -9, d) -6, and e) -2