Question

F(x) = - |x| +4 Define the key features of the graph to the provided absolute value function

Answer 1

Answer:

1. The minus before the |x| reflects the function in the x-axis. So it will still be V-shaped but instead but refected in the x-axis.

2. The +4 moves the function vertically 4 units upwards.

Step-by-step explanation:

We are given the function  f(x) = - |x| +4. We know that the function f(x) = |x| only has positive values, so when x>0 the function is a straight line as in the function f(x) = x. When x<0 the function is also positive, as in the function f(x) = -x. So the graph is V-shaped with the vertex at the origin.

The f(x) = - |x| +4 has two important caracteristics:

1. The minus before the |x| reflects the function in the x-axis. So it will still be V-shaped but instead but refected in the x-axis.

2. The +4 moves the function vertically 4 units upwards.

So the graph of f(x) = - |x| +4 will be V-shaped, reflected in the x-axis and moved 4 units upwards.

Attached you can find the graph