What happens to these curves?

Question

From y=f(x) what happens to:

y=f(x+1)
y=2f(x)
y=f(1/2 x)

Answer 1

y = f(x)

For y = f(x + 1), the original graph f(x) gets shifted 1 unit to the LEFT. Rule of thumb: Any number that is INSIDE the function is a horizontal shift; if it's positive, it's that much to the left, and if it's negative, it's to the right.

For y = 2f(x), the graph gets stretched vertically. Any time there's a number multiplied outside the function, it will affect the graph vertically.

For y = f(1/2 x), the graph will get compressed horizontally. Any time you have a number multiplied INSIDE the function, it will affect the graph horizontally.

Missing from the examples is, for y = f(x)

y = f(x) - 1

In this case, the curve f(x) gets shifted vertically down by one unit. Any time you have a number added/subtracted OUTSIDE of the function, it will affect the vertical shift. Key thing to know is how this contrasts with the horizontal shift; here, a minus sign actually means shifting down, and a plus sign means shifting up, whereas for f(x - 1), we're shifting to the right (contrary to what we might initially believe), and f(x + 1) is shifting to the left.

Answer 2

y= f(x+1) looks like y=f(x), but shifted to the left by one unit.
For example, if f(x) = x^2 then y = (x+1)^2 has its minimum at x= -1 instead of x=0.

y=f(2x) looks like an HD TV channel watched on a regulat TV: squished horizontally so things look taller (and deeper) than they would normally look.

y = f(1/2x) is twice as wide as f(x)

Answer 3

1) shifts to the left
2) gets 2 times bigger
3) is narrowed

Answer 4

Sounds like you just explaine the curved penis syndrome