Question

The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x).

Answer 1

Answer:

  g(x) = |x| -9

Step-by-step explanation:

In the form ...

  g(x) = a|x -h| +k

the parameters are ...

• a: the vertical scale factor (1)
• h: the right shift of the vertex (0)
• k: the upward shift of the vertex (-9)

The vertex of |x| is (0, 0). The vertex of g(x) is (0, -9), so there has been a vertical shift of -9 and no horizontal shift. The slopes of the lines on the graph of g(x) have a magnitude of 1, so the vertical scale is not changed from the original function (a=1).

Then the translated function is ...

  g(x) = |x| -9