Video: Identifying the Graph of a Translated Function

Given the graph of 𝑦 = 𝑔(π‘₯), which of the following is the graph of 𝑦 = 𝑔(π‘₯ βˆ’ 3). [A] Graph a [B] Graph b [C] Graph c [D] Graph d.

01:23

Video Transcript

Given the graph of 𝑦 equals 𝑔 of π‘₯, which of the following is the graph of 𝑦 equals 𝑔 of π‘₯ minus three?

We’re taking our function and subtracting a constant value of π‘˜. And this represents a shift to the right π‘˜ units. What would shifting our 𝑔 of π‘₯ function to the right three units look like?

First, we need to consider our scale. We have an indication at two and a half. Between zero and two and a half, there are five dashes. If we divide two and a half by five, we realise that each mark represents half of a unit. And that means the graph of 𝑔 of π‘₯ has a point at two, zero. It’s half behind two and a half. If our function has a point at two, zero and we need to shift that three units to the right, two plus three equals five, we need graph a.

Graph a has the point five, zero. Graph a is the graph of 𝑔 of π‘₯ shifted three places to the right.

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