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Video: Finding the Point of 𝑦-Intersection of an Exponential Function

Kathryn Kingham

Determine the point at which the graph of the function 𝑓(𝑥) = 6^𝑥 intersects the 𝑦-axis.

01:16

Video Transcript

Determine the point at which the graph of the function 𝑓 of π‘₯ equals six to the π‘₯ 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 π‘₯-value equals zero. So for our function, 𝑓 of π‘₯ equals six to the π‘₯, we want to plug in zero for the π‘₯-value and see what happens.

In this case, we plug in zero for our π‘₯ and we now have the equation six to the zero power. And anything to the zero power is one. For the function 𝑓 of π‘₯ equals six to the π‘₯ power, it crosses the 𝑦-axis when π‘₯ is zero and 𝑦 equals one. Or β€” in coordinate form β€” zero, one.