Graph Question?

Question

Compare the graph of h(x) to the graph of f(x). Explain the transformation in words h(x = f (x+2) -3.

Answer 1

If h(x) = f(x+2) - 3, then h(x) is the same as f(x) shifted 2 to the left and 3 down.

Answer 2

y=f(x)+c, shift the graph of y=f(x) a distance c units upwards
y=f(x) - c, shift the graph of y=f(x) a distance c units downwards
y=f(x-c), shift the graph of y=f(x) a distance c units to the right
y=f(x+c), shift the graph of y=f(x) a distance c units to the left
y=cf(x), stretch the graph of y=f(x) vertically by a factor of c
y=(1/c)f(x), compress the graph of y=f(x) vertically by a factor of c
y=f(cx), compress the graph of y=f(x) horizontally by a factor of c
y=f(x/c), stretch the graph of y=f(x) horizontally by a factor of c
y= --f(x), reflect the graph of y = f(x) about the x-axis
y=f(-x), reflect the graph of y=f(X) about the y-axis

when you have an inverse function the graph of the inverse is a reflection in the y=x line of the original function.

and finally when adding two function f(x+z) you can just add the values of y at each similar value of x and get the new (x,y) co-ordinate.

Answer 3

h is f shifted by 2 units to the left and 3 units down.