Every exponential function is strictly increasing. True or false? Explain
False. Every exponential function is not strictly increasing.
An exponential function of the form f(x) = a^x, where a is a positive constant, can be either strictly increasing or strictly decreasing, depending on the value of the base (a).
If the base (a) is greater than 1, then the exponential function is strictly increasing. As x increases, the value of a^x also increases.
However, if the base (a) is between 0 and 1, then the exponential function is strictly decreasing. As x increases, the value of a^x decreases.
Therefore, the statement that every exponential function is strictly increasing is false. It depends on the value of the base (a) in the function.
False. Not every exponential function is strictly increasing. An exponential function is a mathematical function of the form y = a^x, where a is a positive constant.
To determine whether an exponential function is strictly increasing, we need to examine the value of the base 'a'. If a is greater than 1, then the exponential function will be strictly increasing. This is because, as x increases, the value of a^x will increase at an increasing rate.
However, if the base 'a' is between 0 and 1, then the exponential function will be strictly decreasing. In this case, as x increases, the value of a^x will decrease at a decreasing rate.
Moreover, when the base 'a' is equal to 1, the exponential function will be constant. This means that regardless of the value of x, the output of the function will remain the same.
Therefore, the statement "every exponential function is strictly increasing" is false. It depends on the value of the base 'a' in the function y = a^x.