Level 567 Level 569
Level 568

Vertical & Horizontal Shifts, Stretches & Reflecti


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y = f(x) + c
Shift the graph of y = f(x) a distance c units upward
y = f(x) - c
Shift the graph of y = f(x) a distance c units downward
y = f(x - c)
Shift the graph of y = f(x) a distance c units to the right
y = f(x + c)
Shift the graph of y = f(x) a distance c units to the left
y = cf(x)
Stretch the graph of y = f(x) vertically by a factor of c
y = (1/c)f(x)
Shrink the graph of y = f(x) vertically by a factor of c
y = f(cx)
Shrink the graph of y = f(x) horizontally by a factor of c
y = f(x/c)
Stretch the graph of y = f(x) horizontally by a factor of c
y = -f(x)
Reflect the graph of y = f(x) about the x-axis
y = f(-x)
Reflect the graph of y = f(x) about the y-axis
-f(x)
REFLECT about the X-AXIS
f(-x)
REFLECT about the Y-AXIS
c*f(x)
STRETCH VERTICALLY by a factor of c
f(cx)
COMPRESS HORIZONTALLY by a factor of c
(1/c)*f(x)
COMPRESS VERTICALLY by a factor of c
f(x/c)
STRETCH HORIZONTALLY by a factor of c
f(x)+c
SHIFT C units UPWARD
f(x)-c
SHIFT C units DOWNWARD
f(x-c)
SHIFT C units to the RIGHT
f(x+c)
SHIFT C units to the LEFT
horizontal line
r = k csc θ (or rsinθ = k or y = k or r = k/sinθ)
Equation of the x-axis
Since it's a horizontal line, the equation for the x-axis is y = 0.
vertical line
r = h sec θ (or rcosθ = h or x = h or r = h/cosθ)
Equation of the y-axis
Since it's a vertical line, the equation for the y-axis is x = 0.