Question

The graph of g is the graph of f translated horizontally 3 units to the left. If f(x) = 2x + 1 what is an equation for the function g?

Group of answer choices

g(x) = 3(2x + 1)

g(x) = 2(x + 3) + 1

g(x) = 2(x – 3) + 1

g(x) = 2x + 1 + 3

Answer 1

Answer: g(x) = 2(x + 3) + 1

Explanation:

When we have an horizontal translation of A units (A is a positive real number) to the right, we write this as:

g(x) = f(x - A)

If the translation is to the left, then we have:

g(x) = f(x + A).

In this case, we have a translation to the left, and A = 3, then:

g(x) = f(x + 3)

And we know that:

f(x) = 2x + 1

g(x) = f(x + 3) = 2*(x + 3) + 1 = 2x + 6 + 1 = 2x + 7

g(x) = 2x + 7