Question

given the f(x)=x2 write the equation function g(x) whose graph is a translation 5 units left and 3 units down

Answer 1

When a function is translated, it means the function is moved away from its original position.

The function g(x) is: $g(x) = (x + 5)^2 - 3$

Give that:

$f(x) = x^2$

The rule of translation 5 units left is:

$(x,y) \to (x + 5, y)$

So, we have:

$f'(x) = (x + 5)^2$

The rule of translation 3 units down is:

$(x,y) \to (x, y-5)$

So, we have:

$g(x) = (x + 5)^2 - 3$

Hence, the function g(x) is: $g(x) = (x + 5)^2 - 3$

Read more about translations at:

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