The graph of h is a translation 8 units up and 3 units right of the graph of f(x)= x^2 −3x . for each value of x, g(x) is 125% of h(x). write a rule for g .

Using translation concepts, it is found that the rule for g is given by:

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The rule for f is given by: Shifting a function a units up is the same as adding a to the rule, thus, shifting f(x) 8 units up:

Shifting a function f(x) a units to the right is finding f(x - a), and thus, shifting the shifted function given by f(x) + 8, 3 units to the right to find the rule for h:

g(x) is 125% of h(x), thus:

Which is the rule for g.

A similar problem is given at link

You make such translations with graph of the function

a translation 8 units up, then a translation 3 units right, then

If for each value of x, g(x) is 125% of h(x), then you should multiply the function h(x) by coefficient 1.25, then

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