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Determine the point at which the graph of the function 𝑓(𝑥) = 6^𝑥 intersects the 𝑦-axis.
Determine the point at which the graph of the function 𝑓 of 𝑥 equals six to the 𝑥 intersects the 𝑦-axis.
Let’s think about this for a minute. At what point does a function cross the 𝑦-axis? Here’re two examples of functions crossing the 𝑦-axis. They both cross the 𝑦-axis when their 𝑥-value equals zero. So for our function, 𝑓 of 𝑥 equals six to the 𝑥, we want to plug in zero for the 𝑥-value and see what happens.
In this case, we plug in zero for our 𝑥 and we now have the equation six to the zero power. And anything to the zero power is one. For the function 𝑓 of 𝑥 equals six to the 𝑥 power, it crosses the 𝑦-axis when 𝑥 is zero and 𝑦 equals one. Or — in coordinate form — zero, one.
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