# Do the following equations define functions: (i) #y = x^2-5x# (ii) #x = y^2-5y# ?

##### 1 Answer

Mar 4, 2017

See explanation...

#### Explanation:

**First equation: #y = x^2-5x#**

For the first equation, putting

#y = x^2-5x = (-6)^2-5(-6) = 36+30 = 66#

Note that the value of

graph{(y - x^2+5x)(x+6+0.0001y) = 0 [-11, 11, -11, 102]}

**Second equation: #x = y^2-5y#**

For the second equation, putting

#-6 = x = y^2-5y#

Adding

#0 = y^2-5y+6 = (y-2)(y-3)#

So

Note that

graph{(x - y^2+5y)(x+6+0.0001y) = 0 [-12, 2, -2.5, 6]}