Transformations pre calc

y = g(x+2)

Shifted left by two units

y = g(x-2)

Shifted right by two units

y = g(x)+2

shifted up by two units

y = g(x) - 2

shifted down by two units

y = 2g(x)

vertically stretched (stretches away) by a factor of two

y = 1/2g(x)

Vertically compressed by a factor of two

• it widens

y = -g(x)

Reflected across the x-axis

y = g(-x)

reflected across the y axis

y = g(2x)

horizontally compressed by a factor of two

y = g(1/2x)

horizontally stretched by a factor of two

f(x) = 2 |x+4| - 1

• down one

• Left by 4

• Stretch by 2 (gets narrower)

f(x) = -3 |x+3| -1

• down by 1

• Left by 3

• Reflection across the x-axis (affects y)

• Stretches by 3 (gets narrower)

f(-x - 5) -4

• down 4

• left 5

• reflected across y-axis

f(-x-5)

• take out gcf

  • f(-(x+5)

    • reflected across the y-axis

    • left 5

Inside parenthesis

horizontal, x

outside parenthesis

vertical, y