Answer:
The end behavior of the function is that it approaches positive infinity as x decreases to negative infinity, and it also approaches positive infinity as x approaches positive infinity.
Explanation:
The end behavior of a function is what happens to the value of the function as x approaches negative infinity and as x approaches positive infinity.
Graphing the function is very helpful to visualize the end behavior.
Here, the graph has the shape of a V with the vertex on the x-axis going up in value on both sides forever.
The function here is f(x) = 3|x|.
Let's try a few values for x to get an idea.
We will deal with x approaching positive infinity first.
f(0) = 3|0| = 0
Let's get larger and larger values for x, approaching positive infinity.
f(10) = 3|10| = 30
f(10,000) = 3|10,000| = 30,000
f(1,000,000) = 3|1,000,000| = 3,000,000
As you can see, as x increases, the value of f(x) also increases. As x approaches positive infinity, f(x) also approaches positive infinity.
Now let's look at values of x approaching negative infinity.
f(0) = 3|0| = 0
Let's get smaller and smaller values for x, approaching negative infinity.
f(-10) = 3|-10| = 30
f(-10,000) = 3|-10,000| = 30,000
f(-1,000,000) = 3|-1,000,000| = 3,000,000
As you can see, as x decreases, the value of f(x) increases. As x approaches negative infinity, f(x) approaches positive infinity.
The end behavior of the function is that it approaches positive infinity as x decreases to negative infinity, and it also approaches positive infinity as x approaches positive infinity.