Shifts in graphs

Question

Describe shift(s) that can be applied to the graph of f(x)=1/x

a) 1/(x+8)

b) (1/x)+3

c) (1/x)-1/5

d) 1/(x-2)-ln7

Answer 1

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

1. y = f(x) + C  Raises the graph up the y axis by an amount = C
2. y = f(x) - C   Lowers 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) = 1/x , so 1/(x-8) = f(x-8), so rule 4 applies.  The function is shifted 8 units to the right along the x-axis

 

b)   f(x) = 1/x, so (1/x)+3 = is f(x)+3, so rule 1 applies

 

c)   is similar to b) except the value is negative so rule 2 applies

 

d)  Two rules apply here.  Can you figure out which ones?  Remember, ln7 is just a constant.  Let me know in the comments and I'll let you know if you're right.