Given the graph of 𝑦 equals 𝑔 of
𝑥, which of the following is the graph of 𝑦 equals 𝑔 of 𝑥 minus three?
We’re taking our function and
subtracting a constant value of 𝑘. And this represents a shift to the
right 𝑘 units. What would shifting our 𝑔 of 𝑥
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
𝑥 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 𝑥
shifted three places to the right.