Question

Help?

What is the equation of the function y=5/x translated 4 units to the left and 3 units up?

I don't even know where to start to do this, a little confused on the process to calculate?

Answer 1

use this link to graph the equation

then change some values to see the effect they have on the graph

https://www.desmos.com/calculator

Answer 2

@cambell_st ok, i'll try it out

Answer 3

so the easiest place to start is with the vertical shift. these are always fairly straight forward as you can just add whatever shift you want onto the equation and it'll happen.
for example here, since you want to shift the function up 3 units, you are essentially saying at any given point, i want y to be 3 units higher than usual. You can achieve this by adding 3 to your function. so that would give you:
y=5/x + 3
simple enough right?

now for the horizontal shift its slightly trickier as it can be a little counter intuitive.
essentially what shifting something left or right means is that you want to take every single point you have and move it to a new x position by a certain amount. in your case, to move something left by 4 units, you want a your function to behave as its parent function would if it were 4 points over. you can achieve this by adding or subtracting a value directly from x.

if it helps, you can always plug in various points and think about what they should do. in this case we want x=1 from the parent function to be shifted left by 4. at x=1,y=5
if you shift the point (1,5) left by 4, you get the point (-3,5)

alternatively, to get from the new function you have to add 4 to the x value to get back to the parent function. so if you add 4 to x in your equation, you will get a leftward shift by 4

this leaves you with the final equation y=5/(x+4) + 3

Answer 4

@lifeengineer thank you so much!

Answer 5

no worries @finepetite325 !