Question

The graph shows g(x), a transformation of f(x)=|x|. Write the function rule for g(x).
Write your answer as a|x–h|+k, where a, h, and k are integers or simplified fractions.

Answer 1

Answer:

g(x) = - | x | + 7

Step-by-step explanation:

the standard form of the absolute value function is

g(x) = a | x - h | + k

(h, k ) are the coordinates of the vertex and a is a multiplier

here coordinates of vertex (h, k ) = (0, 7 ) , then

g(x) = a | x - 0 | + 7

to find a , substitute the coordinates of any point on the graph into the equation.

using (- 3, 4 )

4 = a | - 3 - 0 | + 7 ( subtract 7 from both sides )

- 3 = a | - 3 | = 3a ( divide both sides by 3 )

- 1 = a

Then

g(x) = - | x | + 7