Level 567
Level 569

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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.