how do you graph F(-x)-3

Question

i need to know how to graph F(-x)-3 

 

as well as 

 

-F(x+2)

 

Answer 1

Assume you have a function, y = f(x) and its graph.

 

y = f(-x)-3 is a couple of transformations of y = f(x).

 

If x is changed to -x the graph is reflected over x = 0, the y-axis.

 

If y is changed to y - k the graph is shifted k units in the y direction.

 

Let's add 3 to both sides of your function:

 

y + 3 = f(-x)

 

Compare to y = f(x).

 

y → y - (-3), so the graph is shifted down 3 units.

 

x → -x, so the graph is reflected over x = 0, the y-axis.

 

=====

 

y = -f(x+2)

 

or -y = f(x+2)

 

Compare to y = f(x);

 

y → -y so graph is reflection of f(x) over y = 0, the x-axis.

 

x → x+2 = x-(-2) so graph is f(x) shifted left 2.