Difference between horizontal and vertical graph transformations

[DizzyDoo]

Some questions about transforming graphs that I would like a hand with. I've given them educational guesses, but if someone could take a look at them, that would be great.

Homework Statement

2. Explain the difference in the transformations to the graph of f(x) by f(x+2) and f(x)+2.

3. Explain the difference in the transformations to the graph of f(x) by f(3x) and 3f(x).

5. Explain how to find an equation of the normal to a curve at a given point.

Homework Equations

None

The Attempt at a Solution

For (2) f(x+2) would stretch the graph along the X axis by x2, right? Where as f(x)+2 would just nudge the graph along the X axis by 2 points.

But for (3) I'm really not sure what the difference is (obviously there is a significant one) of the 3 being inside the brackets or out. Any help here?

For (5)... I'm a little stuck. I'm thinking that I might have to differentiate to start with, but I'm not entirely sure.

Thanks for taking the time to look at this.

 

[Leong]

5.
1.differentiate
2. find the slope/gradient (tangent line)
3. find the normal gradient (tangent slope x normal slope = -1)
4. the coordinate of one point and the normal gradient are known, proceed with finding the line equation.

 

[Leong]

2.

f(x+2) : move the original graph two units to the left

f(x) + 2 : move the original graph two units upwards