Question

Which of the following statements is true about the graphs of f(x) = x and g(x) = f(x+7)?

A) g(x) is the graph of f(x) translated 7 units down
B) g(x) and f(x) have the same y-intercept
C) g(x) is the graph of f(x) translated 7 units to the left
D) g(x) is the graph of f(x) translated 7 units to the right

Answer 1

The correct statement is C) g(x) is the graph of f(x) translated 7 units to the left.

Step-by-step explanation:

The correct answer is C) g(x) is the graph of f(x) translated 7 units to the left.

To understand why, let's break down the given functions:

f(x) = x represents a linear function with a slope of 1 and a y-intercept of 0. This means that for every unit increase in x, there is a corresponding unit increase in y.

g(x) = f(x+7) represents the same function as f(x), but with x shifted 7 units to the left. This means that for every value of x in f(x), the corresponding value of x in g(x) is 7 units less.

Therefore, g(x) is the graph of f(x) translated 7 units to the left.