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Video: Finding the Point at Which a Constant Function Intersects the 𝑥- or 𝑦-Axes

Kathryn Kingham

Find the point at which the function 𝑓(𝑥) = 12 intersects either the 𝑥 or 𝑦 axis.


Video Transcript

Find the point at which the function 𝑓 of π‘₯ equals 12 intersects either the π‘₯- or 𝑦-axis.

Our function, 𝑓 of π‘₯ equals 12, what does that mean? What does a graph of 𝑓 of π‘₯ equal 12 look like? Here’s what we’re going to do. We’re going to plug in some values of π‘₯ to our function to see what happens.

If 𝑓 equals one in this function, what is the output? What is the solution? 12, because 𝑓 of π‘₯ always equals 12 in this function. And when the π‘₯-value is negative one, the solution is still 12. So I’ll just add some numbers to my graph here and sketch this out. So now we found two points. 𝑓 at one equals 12; there is that point. 𝑓 at negative one also equals 12. If we plugged in 𝑓 of 10, we still have 12.

Are you seeing a pattern here? The function 𝑓 of π‘₯ equals 12 represents a horizontal line at 12. Now our question wants to know where does this function intersects the π‘₯- or the 𝑦-axis. We can tell that it does not intersect the π‘₯-axis. And there is the point where it intersects the 𝑦-axis. At point or co-ordinate zero, 12, the function 𝑓 of π‘₯ equals 12 intersects the 𝑦-axis.