Question

Which rule represents the transformation of f(x) = -3x + 7 after a horizontal shift 1 unit left to form g(x)?

A) g(x) = -3(x + 1) + 7
B) g(x) = -3(x - 1) + 7
C) g(x) = -3x + 6
D) g(x) = -3x + 8
E) g(x) = -3x + 7

Answer 1

The function representing a horizontal shift 1 unit left of f(x) = -3x + 7 is g(x) = -3(x + 1) + 7. However, none of the given options correctly reflects the simplified form after applying the shift, which should simplify to g(x) = -3x + 4, hence, the closest correct option listed is A) g(x) = -3(x + 1) + 7.

Step-by-step explanation:

The question is asking about a transformation of a linear function, specifically a horizontal shift. Given the original function f(x) = -3x + 7, a horizontal shift 1 unit left would be represented by changing x to x + 1 inside the function. This results in g(x) = -3(x + 1) + 7, simplifying to g(x) = -3x -3 + 7, which then simplifies further to g(x) = -3x + 4. However, this option does not appear among the choices given. If we look at the options, only Option A has the correct form that shows a 1 unit left shift (i.e., x is replaced by x + 1).