Questions: Which are true of the function (f(x)=49(1/7)^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.

Solution Steps

The function given is \( f(x) = 49\left(\frac{1}{7}\right)^{x} \). This is an exponential function. The domain of an exponential function is the set of all real numbers because you can substitute any real number for \( x \) and get a valid output.

For the function \( f(x) = 49\left(\frac{1}{7}\right)^{x} \), the base of the exponential is \(\frac{1}{7}\), which is a positive number less than 1. As \( x \) approaches positive infinity, \( f(x) \) approaches 0 from the positive side. As \( x \) approaches negative infinity, \( f(x) \) approaches infinity. Therefore, the range of the function is \( y > 0 \).

The function \( f(x) = 49\left(\frac{1}{7}\right)^{x} \) is a decreasing exponential function. As \( x \) increases by 1, the value of \( f(x) \) is multiplied by \(\frac{1}{7}\). This means each \( y \)-value is one-seventh of the previous \( y \)-value.

Final Answer