Question

Find g(x), where g(x) is the translation 6 units left of f(x) = x².

Write your answer in the form a(x - h)+k, where a, h, and k are integers.

Answer 1

The function g(x) can be expressed as g(x) = a(x - h) + k, where a is the coefficient of x (which is 1 for f(x) = x^2), h is the horizontal shift, and k is the vertical shift.

To translate a function 6 units left, we need to shift it horizontally by -6 units. So, h = -6.

Since the function g(x) is a translation of f(x), a and k will have the same values as in f(x). In this case, a = 1 and k = 0.

Therefore, the function g(x) that represents the translation 6 units left of f(x) is:

g(x) = a(x - h) + k

= 1(x - (-6)) + 0

= 1(x + 6) + 0

= x + 6

the answer is: g(x) = x + 6