Question Video: Identifying the Coordinates of Points Following a Transformation | Nagwa Question Video: Identifying the Coordinates of Points Following a Transformation | Nagwa

# Question Video: Identifying the Coordinates of Points Following a Transformation Mathematics • Second Year of Secondary School

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The figure shows the graph of π¦ = π(π₯) and the point π΄. The point π΄ is a local maximum. Identify the corresponding local maximum for the transformation π¦ = π(π₯ β 1) + 4.

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### Video Transcript

The figure shows the graph of π¦ equals π of π₯ and the point π΄. The point π΄ is a local maximum. Identify the corresponding local maximum for the transformation π¦ equals π of π₯ minus one plus four.

We need to recall firstly what types of transformations are represented by π of π₯ minus one plus four. Firstly, we recall that π of π₯ plus π is a translation of π of π₯ π units in the positive π¦-direction. So, when weβre adding a constant to the overall function, this is a vertical translation by that amount. It simply shifts the graph up or down by the value of the constant π. So, adding four on the end of the function here means that we are translating π¦ equals π of π₯ four units up.

But weβve also got something happening inside the parentheses to the input of the function because we have π of π₯ minus one. We should recall then that when a change is happening to the input to the function itself, this has a horizontal effect. π of π₯ minus π is a translation π units in the positive π₯-direction. Itβs a horizontal shift this time. So, π of π₯ minus one means that the graph is being translated one unit in the positive π₯-direction. Thatβs one unit to the right. So, we could say that this transformation is a translation one unit right and four units up, or we could say that weβre translating by the vector one, four.

Either way, we need to consider what the impact is specifically on this point π΄ which has coordinates two, one. If we translate this point one unit right and then four units up, we arrive at a new point here which we can think of as π΄ prime. The coordinates of this point are three, five. To achieve the horizontal translation, weβve added one to the π₯-coordinate of two. And to achieve the vertical translation, weβve added four to the π¦-coordinate of one. So, we find that the corresponding local maximum for the transformation π¦ equals π of π₯ minus one plus four is the point three, five.

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