Question 1164851
to shift the graph vertically upward, you need add a constant to the end of it.


so, if your equation is f(x), then your new equation has to be f(x) + a, where is a positive constant.


to shift the graph horizontally to the right, you need to subtract a constant from the variable used.


so, if your equation is f(x), then your new equation has to be f(x-a), where a is a positive constant.


for example:


consider the equation of f(x) = x^2


f(x) + 5 = x^2 + 5 shifts the equation up 5 units.


this means that the value of y for the same value of x is 5 units more positive than the original equation.


you can see on the graph, that, in the equation of y = x^2, y = 0 when x = 0.


you can also see on the graph, that, in the equation of y = x^2 + 5, y = 5 when x = 0.


in the graph, y = x^2 is red and y = x^2 + 5 is blue.


now consider the equation of  f(x) = x^2 again.


f(x-5) = (x-5)^2 shift the equation to the right  5 units.


this means that the value of x for the same value of y is 5 units to the right of the original equation.


you can see on the graph that, in the equation of y = x^2, x = 0 when y = 0.


you can also see on the graph that, in the equation of y = (x-5)^2, x = 5 when y = 0.


in the graph, y = x^2 is red and y = (x-5)^2 is green.


here's the graph.


<img src="http://theo.x10hosting.com/2020/091401.jpg" >


note that the use of f(x) and the use of y is interchangeable.


that's because f(x) = y.


you can say y = x^2 and you can say f(x) = x^2 and it means the same thing.