Question

What effect does replacing x with x + 2 have on the graph for the function f(x) ?

f(x)=|x−3|+2



The graph is shifted 2 units left.
The graph is shifted 2 units down.
The graph is shifted 2 units right.
The graph is shifted 2 units up.

Answer 1

The graph is shifted 2 units left.

Explanation:

I took the test.

Answer 2

Explanation:

The vertex of f(x)=|x−3|+2 is at (3, 2).

Replacing x with x+2 results in g(x) = f(x)=|(x+2)−3|+2, or

g(x) = f(x)=|x+2−3|+2, or

g(x) = f(x)=|x - 1|+2 The vertex of this graph is at (1, 2).

The effect of replacing x with x + 2 is a horizontal shift to the left, of 2 units, of the original graph.