Subjects algebra

Exponential Function 93B3De

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1. The problem asks us to identify which of the given functions is an exponential function. 2. Recall the definition: An exponential function has the form $$y = a^x$$ where the base $$a$$ is a positive constant not equal to 1, and the variable $$x$$ is in the exponent. 3. Let's analyze each function: - For $$y = x^2$$, the variable $$x$$ is the base and the exponent is a constant 2. This is a polynomial function, not exponential. - For $$y = 9^x$$, the base is 9 (a positive constant) and the variable $$x$$ is in the exponent. This matches the form of an exponential function. 4. Therefore, $$y = 9^x$$ is an exponential function. 5. Graphically, $$y = x^2$$ is a parabola opening upwards, while $$y = 9^x$$ is an exponential curve that grows rapidly for positive $$x$$ and approaches zero for negative $$x$$. Final answer: The exponential function is $$y = 9^x$$.