Algebra 2. Translating f(x) g(x)

Question

f(x) = x- 5 translate 4 units to the left

How do you translate the graph 4 units to the left 

Answer 1

Hi Emma!

There's a few ways to do this!

You could do it graphically. You'd start by graphing the original function, f(x)=x-5. Then move each point you plotted left four units on your graph.

OR

You could do it algebraically. To do this, the first think you need to remember is to translate a function left means going from f(x) = x to f(x) = (x+h). Note that +h inside the parenthesis is what moves the function to the LEFT on a graph. Applying this tp your question: we start with f(x) = x-5. To find g(x), or f(x) translated 4 units left, we can substitute in g(x) = f(x+4). Remember that +4 is what moves the graph 4 units LEFT.

From here we just need o simplify further! g(x) = f(x+4) = (x+4)-5 = x-1. And your equation for the translated function is g(x)=x-1!

Hope this helps!

Answer 2

g(x) = f(x+4) = (x+4)-5 = x-1