Question

Find g(x), where g(x) is the translation 6 units left and 14 units up of f(x)= -2x+6. Write your answer in the form mx+b, where m and b are integers?

Answer 1

To find g(x) as a translation of f(x) = -2x + 6, we apply the translations resulting in g(x) = -2(x+6) + 6 + 14, which simplifies to g(x) = -2x + 8.

Step-by-step explanation:

The student has asked to find the function g(x), which is derived from f(x) = -2x + 6 by translating it 6 units to the left and 14 units up. A translation to the left means we will replace x with (x+6), and translating up adds 14 to the whole function. Using these transformations, we get:

g(x) = f(x+6) + 14

= -2(x+6) + 6 + 14

= -2x - 12 + 20

= -2x + 8

Therefore, the equation of the function g(x) after the translation is -2x + 8.