Question

Find g(x), where g(x) is the translation 1 unit left of f(x)=2x+6.

a) g(x) = 2x + 5
b) g(x) = 2x + 7
c) g(x) = 2x + 4
d) g(x) = 2x + 8

Answer 1

To find g(x), the translation 1 unit left of f(x) = 2x + 6, you add 1 to the variable within f(x). After applying the transformation, the function becomes g(x) = 2x + 8.

Step-by-step explanation:

The question involves finding the function g(x), which is the translation 1 unit left of the given function f(x) = 2x + 6. To translate a function to the left by 1 unit, you add 1 to the variable inside the function. Therefore, g(x) = f(x + 1), which means we substitute x + 1 for x in f(x).

g(x) = f(x + 1) = 2(x + 1) + 6 = 2x + 2 + 6 = 2x + 8.

Thus, the correct answer is d) g(x) = 2x + 8.