Final answer:
The domain of the exponential function h(x) = -343^x is all real numbers, while the range is all negative real numbers. As x increases, h(x) decreases due to the negative base, causing an exponential decay. As x decreases, h(x) increases in magnitude, moving it toward zero due to the effect of negative exponents.
Step-by-step explanation:
When analyzing the exponential function h(x) = −343^x, the domain represents all the possible input values for x. In this case, x can be any real number, meaning there are no restrictions on the value that x can take. Thus, the domain of h(x) is all real numbers.
The range of an exponential function is determined by the set of possible output values. Since the exponential function never touches the y-axis due to the negative base, the range is all real numbers except for zero. More specifically, because the base is negative, the function will produce negative values for all x, which means the range is restricted to negative real numbers.
Concerning the behavior of the exponential decay as x increases or decreases, recall the nature of exponents. As x increases, the value of −343^x becomes smaller, which means h(x) decreases. Conversely, as x decreases, h(x) increases in magnitude as the negative exponent makes the negative base smaller in absolute value but negative sign keeps it below zero.
The understanding of the inverse relationship between natural logarithms and exponentiation can shed light on this concept. In this case, however, the concept of a negative base replaces the typical growth pattern of an exponential function with an exponential decay.