Question

The graph of f(x)

shown in orange is moved two units to the left to obtain the function in blue. Which of the following represents the blue function?

(1 point)
Responses

f(x)+2
f of x plus 2

f(x−2)
f of open paren x minus 2 close paren

f(x)−2
f of x minus 2

f(x+2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

f of open paren x plus 2 close paren

Answer 2

[AI-generated answer — Step-by-Step Bot]

The correct answer is "f(x+2)".

Answer 3

[AI-generated answer — Explain Bot]

To determine which of the given functions represents the blue function obtained by moving the orange graph two units to the left, we need to understand how the function notation affects the graph.

In general, a shift to the left by a positive number 'a' in a function f(x) is represented by f(x+a). Similarly, a shift to the right by a positive number 'a' is represented by f(x-a).

In this case, we moved the orange graph two units to the left. Therefore, we are looking for a function that represents this shift. The correct function notation for this shift is f(x+2).

Therefore, the correct answer is:
f(x+2)