With this quickly

f(x) = - |x| + 4
in complete sentences to answer the following prompts.

a. define the key features of the graph of the provided absolute value function.
b. provide the coordinate of the vertex and two additional points on the graph.
c. use the coordinate of the function’s vertex to prove the domain and range of the function.

We are given the function .

Part A: We can see that,

The given function is obtained by applying some transformations to the parent function .

Now, first the function g(x) is reflected across x-axis which given the function .

The, this function is translated 4 units upwards to get .

Thus, the function is reflected across x-axis and then translated 4 units upwards.

Part B: We see that,

At x= 0, the function value is i.e. f(0)= 4

Thus, the vertex of the function is (0,4).

Moreover, when f(x)= 0, the values of x are,

i.e.

i.e. x= 4, -4

So, the two points on the graph are (4,0) and (-4,0).

Part C: From the graph, we see that,

The domain of the function is the set of all real numbers.

Since, the graph is located below the the point (0,4).

Then, the range of the function is .

12/11c

or

12

c

11