• stretches change the shape of the graph of a function
• vertical expansion = taller and skinnier
• vertical compression = shorter and wider
• horizontal expansion = wider
• horizontal compression = skinnier
• vertical expansion is very similar to horizontal compression
• vertical compression is very similar to horizontal expansion

Vertical Expansions and Compressions

• y = af(x)
• if a is greater than 1 or less than -1, vertically expanded
• if a is between -1 and 1, vertically compressed
• if a is negative, vertically reflected (y becomes -y), reflected on the x-axis
• when y = f(x) becomes y = af(x), (x, y) becomes (x, ay)
• the y value represents vertical, so multiply "a" by y

Horizontal Expansions and Compressions

• y = f(bx)
• if b is greater than 1 or less than -1, horizontally compressed
• if b is between -1 and 1, horizontally expanded
• if b is negative, horizontally reflected (x becomes -x), reflected on the y-axis
• when y = f(x) becomes y = f(bx), (x, y) becomes ((1/b)x, y), (multiply by the reciprocal of b)
• the x value represents horizontal, so multiply 1/b by y)