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

2. Transformations of Points f(x – a) 0 (1, 4) (3, 1) Imagine a function where y = f(x), which has a root at 0, and points (1, 4) and (3, 1) lie on the curve: f(x)f(x - 1) 1 (2, 4) (4, 1)

3. Transformations of Points f(x) - a 0 (1, 4) (3, 1) Imagine a function where y = f(x), which has a root at 0, and points (1, 4) and (3, 1) lie on the curve: f(x)f(x) - 4 -4 (1, 0) (3, -3)

4. Transformations of Points nf(x) 0 (1, 4) (3, 1) Imagine a function where y = f(x), which has a root at 0, and points (1, 4) and (3, 1) lie on the curve: f(x)2f(x) 0 (1, 8) (3, 2)

5. Transformations of Points f(nx) 0 (1, 4) (3, 1) Imagine a function where y = f(x), which has a root at 0, and points (1, 4) and (3, 1) lie on the curve: f(x)f(2x) 0 (0.5, 4) (1.5, 1)

6. Transformations of Points -f(x) 0 (1, 4) (3, 1) Imagine a function where y = f(x), which has a root at 0, and points (1, 4) and (3, 1) lie on the curve: f(x)-f(x) 0 (1, -4) (3, -1)

7. Transformations of Points f(-x) 0 (1, 4) (3, 1) Imagine a function where y = f(x), which has a root at 0, and points (1, 4) and (3, 1) lie on the curve: f(x)f(-x) 0 (-1, 4) (-3, 1)