Which statement best describes the effect of replacing the function f(x) = 2x − 2 with the function g(x) = 2x + 3?
The graph shifts 1 units left.
The graph shifts 5 units left.
The graph shifts 1 unit right.
The graph shifts 3 units right.
Plz help
5 units to the left
because you are going
from a -2 to a 3 which is a difference of 5.
Thnx so much
g(x) = f(x)+5, so it is shifted up 5 units.
or,
f(x) = 2x-3
g(x) = 2x+2 = 2(x+5/2)-3
So, g(x) is f(x) shifted left 5/2
To determine the effect of replacing the function f(x) = 2x - 2 with the function g(x) = 2x + 3, we need to analyze the changes in the equation. Specifically, we want to compare how the x-values in the original function (f(x)) relate to the x-values in the new function (g(x)).
In f(x) = 2x - 2, the coefficient of x is 2, indicating that the graph of this function has a slope of 2. Additionally, the constant term -2 shifts the graph vertically downward by 2 units.
In g(x) = 2x + 3, the coefficient of x is also 2, indicating that the graph of this function has the same slope as f(x). However, the constant term +3 shifts the graph vertically upward by 3 units.
Since the constant term determines the vertical shift, we can conclude that by replacing f(x) = 2x - 2 with g(x) = 2x + 3, the graph of the function shifts upward by 3 units. Therefore, the correct statement describing the effect is: "The graph shifts 3 units upward."