compressing/stretching; f(x) = c*g(x), where c is a constant; if this constant is greater than one, then the graph has been vertically stretched. If it is between 0 and 1, then the graph has been vertically compressed.

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.

Some notes:

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).