How do I find the graph of #y=2/(x-1)^2-3#?
1 Answer
Start from the graph of
Explanation:
Start from the graph of
-
Horizontal translation:
#f(x) \to f(x+k)# . Any transformation like this will shift the graph horizontally, to the left if#k>0# , to the right if#k<0# . In this case, we are translating one unit right, because we are transforming
#1/x \to 1/(x-1)# -
Squaring:
#f(x) \to f^2(x)# . This kind of transformations preserves the zero of the function, and reflects the negative parts with respect to the#x# axis, turning them positive. Also, it makes values between#0 and 1# smaller, and values above#1# greater. So far, we have transformed
#1/(x-1) \to 1/(x-1)^2# -
Vertical stretch:
#f(x) \to kf(x)# . This kind of transformations stretches the graph vertically. It expands the graph if#k>1# , and compress it if#0 < k < 1# . If#k<0# , it reflects the function with respect to the#x# axis, and then apply the same logic as above. So far, we have transformed
#1/(x-1) \to 2/(x-1)^2# -
Vertical translation:
#f(x) \to f(x)+k# . This kind of transformations translates the graph vertically, upwards if#k>0# , downwards if#k<0# . In this case, we translate three units down. Finally, we have transformed
#2/(x-1)^2 \to 2/(x-1)^2-3#
