Question

Which statement correctly describes the relationship between the graph of f(x)=x and the graph of g(x)=f(x)+5 ?

The graph of g(x) is the graph of​ f(x)​ vertically stretched by a factor of 5.
The graph of g(x) is the graph of​​​ f(x) translated 5 units up.
The graph of g(x) is the graph of f(x) translated 5 units right.
The graph of g(x) is the graph of​​ f(x)​ vertically compressed by a factor of 5.

Answer 1

Answer: B) f(x) is translated 5 units up

Recall that y = f(x) since both are outputs of a function

Saying f(x)+5 is the same as y+5. So we're adding 5 to each y coordinate of each (x,y) point. A point like (1,7) turns into (1,12) after doing this shifting.

Doing this to every point shifts the entire f(x) curve 5 units up to get g(x)