Question

PLZ HELP):

Describe the graph y=1/2x-10 -3 compared to the graph of y=1/x

i have no idea how to word this properly

Answer 1

We start from the parent function

`y=(1)/(x)`

If we transform
`x\mapsto x-5` we have

`y=(1)/(x-5)`

Every transformation of the form
`f(x)\mapsto f(x+k)` translates the function horizontally, k units to the left if k is positive, k units to the right if k is negative.

So, with this first step, we translate the graph 5 units to the right.

Then, we can transform the function by multiplying it by one half:

`y=(1)/(x-5)\cdot (1)/(2) = (1)/(2(x-5))=(1)/(2x-10)`

Every transformation of the form
`f(x)\mapsto kf(x)` scales the function vertically. The function is squeezed by a factor k if k is between 0 and 1, and it is stretched by a factor k if k is greater than 1.

So, with this second step, we squeeze the function vertically with a factor of 1/2.

Finally, we can transform the function by subtracting three:

`(1)/(2x-10)-3`

Every transformation of the form
`f(x)\mapsto f(x)+k` translates the function vertically, k units up if k is positive, k units down if k is negative.

So, with the last step, we translate the graph 3 units down.

To recap: starting with the graph of the parent function, you translate it 5 units to the right, scale it vertically by a factor of 1/2, and then move it down 3 units.