Now, HORIZONTALLY stretching/compressing occurs when the x values have been multiplied by a constant. That is, f(x) = g(cx); if this constant is greater than one, then the graph has been horizontally compressed. If it is between 0 and 1 then the graph has been horizontally stretched.
Graphs of a function f(x) are said to be reflected (across the y-axis) when the x values of the function have been multiplied by a negative value. And, the graph is said to be reflected (across the x-axis) when the y values of the function have been multiplied by a negative value.
y = f(x) + 10 shifts the graph up 10 units- this affects the y values.
Similarly, y = f(x) - 10 shifts the graph down 10 units.
For example: g(x) = x^2 + 10
A vertical stretch with a factor of 5 is: y = 5*f(x); this multiplies the y values by the constant, 5.
For example: g(x) = 3*sqrt(x)
Vertical compression by a factor of 10: y = 1/10*f(x); this multiplies the y-values by 1/10.
A vertical reflection about the x-axis: y = -f(x)
Horizontal shifts, compressions, etc affect the x values.
A graph shifted 10 units horizontally to the left, a graph shifted 10 units horizontally to the right, a graph stretched horizontally by a factor of 1/10, and a graph compressed by a factor of 5 are all given, respectively, below:
y = f(x + 10)
y = f(x - 10)
y = f((1/10)x)
y = f(5x)
And finally, a horizontal reflection about the y-axis is given by:
y = f(-x)
(Which multiplies the x-values by -1).