transformations of points f(x + a) 0 (1, 4) (3, 1) imagine a function where y = f(x), which has a...

Transformations of Points • f(x + a) 0 (1 , 4) (3, 1) ne a function where y = f(x), which has t at 0, and points (1 , 4) and (3 , 1) lie on the curve: f(x) f(x + 1) -1 (0 , 4) (2, 1)

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Transformations of Points

• f(x + a)

(1 , 4)

(3, 1)

Imagine a function where y = f(x), which hasa root at 0, and points (1 , 4) and (3 , 1) lie on the curve:

f(x) f(x + 1)

-1

(0 , 4)

(2, 1)

Transformations of Points

• f(x – a)

(1 , 4)

(3, 1)

Imagine a function where y = f(x), which hasa root at 0, and points (1 , 4) and (3 , 1) lie on the curve:

f(x) f(x - 1)

(2 , 4)

(4, 1)

Transformations of Points

• f(x) - a

(1 , 4)

(3, 1)

Imagine a function where y = f(x), which hasa root at 0, and points (1 , 4) and (3 , 1) lie on the curve:

f(x) f(x) - 4

-4

(1 , 0)

(3, -3)

Transformations of Points

• nf(x)

(1 , 4)

(3, 1)

Imagine a function where y = f(x), which hasa root at 0, and points (1 , 4) and (3 , 1) lie on the curve:

f(x) 2f(x)

(1 , 8)

(3, 2)

Transformations of Points

• f(nx)

(1 , 4)

(3, 1)

Imagine a function where y = f(x), which hasa root at 0, and points (1 , 4) and (3 , 1) lie on the curve:

f(x) f(2x)

(0.5 , 4)

(1.5, 1)

Transformations of Points

• -f(x)

(1 , 4)

(3, 1)

Imagine a function where y = f(x), which hasa root at 0, and points (1 , 4) and (3 , 1) lie on the curve:

f(x) -f(x)

(1 , -4)

(3, -1)

Transformations of Points

• f(-x)

(1 , 4)

(3, 1)

Imagine a function where y = f(x), which hasa root at 0, and points (1 , 4) and (3 , 1) lie on the curve:

f(x) f(-x)0

(-1 , 4)

(-3, 1)

Closest Points 1 x 1

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