2.5 Horizontal and Vertical Shifts

Required Videos

Here are the required notes for your convenience.

Two graphs may look exactly alike in shape, but differ in their positions within the xy-plane.

Adding or subtracting values from a function will shift the graph of the function on the coordinate plane.

If f is a function and c is a positive constant, then the graph of

$y = f(x) +3$ shifts $f(x)$ up 3 spaces on the y axis

$y = f(x) - 2$ shifts $f(x)$ down 2 spaces on the y axis

$y = f(x+4)$ shifts the graph of $f(x)$ left 4 spaces on the x axis

$y = f(x-3)$ shifts the graph of $f(x)$ right 3 spaces on the x axis

$y = f(x-5) +2$ shifts the graph of $f(x)$ up 2 spaces on the y-axis and right 5 on the x-axis.

If $f(5) = 2$ , $f(2) = 7$ , and $f(-3) = -14$

Find the coordinates for h(x) = f(x) + 5 and g(x) = f(x – 2)