Question

The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x)=x²?

Answer 1

`g(x) = x^2-16x+66`

Explanation:

Given that the graph of g(x) is f(x) translated to the left 8 units and up 2 units.

When translated to left by 8 units we have

`new X = x+8`

Similarly when f(x) is translated up by 2 units we have

f(x) transferred to f(x) -2

Hence new equation would be

`f(x) -2 = (x-8)^2\\Or g(x) = x^2-16x+66`

Thus we get f(x) is transformed into

`g(x) = x^2-16x+66`

Answer 2

The graph of g(x) is f(x) translated to the left 8 units and up 2 units. Eight units left would mean that the x value is added with 3 units to the negative side. Two units up means that f(x) is moved to point 2. Therefore, the equation would be written as follows:

f(x) + 2 = x² - 3

Hope this answers the question.