describe how the graph of each of the following function can be obtained from the graph of y = f(x)?

Question

1) y= -5f (x) + 3
2) y= 4f (1/2x) + 2
3) y= 2f (x+3) - 4

Answer 1

1) moves up 3 units, reflects over the line y = x, and stretches vertically by a factor of 5.
2) moves up 2 units, stretches vertically by a factor of 4, and shrinks horizontally by a factor of 1/2
3) moves down 4 units, moves to the left 3 units, and stretches vertically by a factor of 2

Answer 2

The - sign refects f(x) across the x-axis. The 5 increases the amplitude of each point of the reflection by 5. The plus 3 then moves the result 3 units up in the plus y direction.

Each y value is halved, then multiplied by four. This essentially just multiplies each y value by 2. Then the result is moved up two units.

The graph is shifted left three units. Then each y value is multiplied by 2. Then the result is moved down 4 units.

Answer 3

if x = 0, y = 2 if x = 10, y = 9.5 Connect these 2 coordinates with an infinite straight line.

Answer 4

1. moves up y -axis
2. stretch by factor of 1/2
3. move along x-axis to the left

I think...