Question

What do you think would happen if we graphed g(x)

alongside f(x)?
f(x) = x
g(x) = f(x + 2)
How would the graphs be the same, and how would
they be different?

Answer 1

Graphing g(x) = f(x + 2) alongside f(x) = x would result in two graphs with g(x) shifted 2 units to the left of f(x)

Analysis of the two equations

Shift to the Left: The function g(x) = f(x + 2) indicates a horizontal shift of the graph of f(x) = x to the left by 2 units. This is because of the +2

Other features such as slope, and shape will remain same

Another difference will be in the y-intercept. the both graphs will have a different y intercept