For each of these statements, decide whether it is true or false, justifying your answer or offering

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For each of these statements, decide whether it is true or false, justifying your answer or offering a counter-example.

a. The graph of y = ax passes through (0, 1) for all positive real numbers a.

b. The function f(x) = ax is always an increasing function for a > 0.

c. The graph of y = ax, where a is a positive real number, never crosses the x-axis.

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