Subjects algebra

Exponential Passing Point

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Exponential Passing Point


1. The problem asks to find the coordinates through which all exponential functions pass. 2. An exponential function generally has the form $$y = a^x$$ where $$a > 0$$ and $$a \neq 1$$. 3. To find common points, we evaluate the function at specific values of $$x$$: - At $$x = 0$$, $$y = a^0 = 1$$ since any nonzero number raised to zero is 1. - At $$x = 1$$, $$y = a^1 = a$$ which varies depending on the base $$a$$. 4. Therefore, regardless of the base, all exponential functions pass through the point $$ (0, 1) $$. 5. Checking the options given: - (0, 1) is correct. - (0, 0) is incorrect. - (1, 0) is incorrect. - (1, 1) is only true for $$a = 1$$, but $$a \neq 1$$ for exponential functions. Hence, the common coordinate is $$\boxed{(0,1)}$$.