Describe the following transformations of the graphs:

Question

x^2 -> (x+4)^2

|x| -> |x|-2

Square Root x ->  Square Root x-3

x^2 -> x^2+1 

Answer 1

For a positive constant, C, here are the rules for transforming a function f(x):

 

1. y = f(x) + C Shifts the graph up the y axis by an amount = C
2. y = f(x) - C Shifts the graph down the y-axis by an amount = C
3. y = f(x + C) Shifts the graph to the left along the x-axis by an amount = C
4. y = f(x - C) Shifts the graph to the right along the x-axis by an amount = C
5. y = -f(x) Reflects the graph of f(x) across the x-axis
6. y = f(-x) Reflects the graph of f(x) across the y-axis
7. y = c*f(x) Stretches (warps) the graph by a factor of c
8. y = (1/c) f(x) Flattens the graph by a factor of 1/c

 

a)  f(x) = x², so (x+4)² = f(x+4) so rule 3 applies

 

b)  f(x) = |x|, so |x| - 2 = f(x) -2 so rule 2 applies

 

c)  f(x) = √x, so √(x-3) = f(x-3) so rule 2 applies

 

d)  (f(x) = x², so x² + 1 = f(x) + 1.  Which rule is that?