Question

The graph of g(x) results when the graph of
f(x) = |x| is shifted 3 units to the left.

Which is the equation of g(x)?

I think its g(x) = |x-3| am I right if im not can you plz explain.

Answer 1

i meant g(x) =- |x - 3|

Answer 2

and its f(x) = -|x| sorry

Answer 3

The answer is actually \[g(x) = -|x-(-3)|\] or, simplifying:\[g(x) = -|x+3|\]Remember that subtraction inside the absolute value bars means that we first subtract that quantity form x, then do the absolute value on that new answer. So to translate f(x) to the left, g(x) will need to subtract a negative 3, or in other words, add 3.

Take for example, the "point" of the V shaped graph. Normally, this is at (0,0). But we want to translate it 3 to the left so that it's at (-3,0). Plug in -3 for x into g(x)=−|x+3|: g(-3) = -1*|-3+3| = -1*|0| = 0. Thus the y coordinate at x=-3 is 0, which is what we wanted, since that means the graph has been moved 3 to the left.

In general, y=|x-h| will be translated h units to the right. If h is negative, there will be a + sign but remember you're subtracting a negative quantity, so then you would move h units to the left.

So to recap, the answer is:
\[g(x) = -|x+3|\]

Answer 4

thank you it makes more sense to me now

Answer 5

g(x)=-|x+3| will move the f(x) to the left 3 units and it will reflect the graph over the x axis.

However, we just want to shift the graph to the left 3 units. We don't want to reflect the graph over the x axis.

So the correct answer is g(x)=|x+3|