Question

The graph of y = f(x) is graphed below. What is the end behavior of f(x)?

Answer 1

The end behavior of f(x) is
`$y\rightarrow\infty$` as
`$x\rightarrow\infty$` and
`$y\rightarrow-\infty$` as
`$x\rightarrow-\infty$` and the correct option is C.

The end behavior of the function $f(x)$ as $x$ approaches positive or negative infinity can be determined by analyzing the dominant term of the function's expression.

The graph of f(x) shown appears to have a dominant term of x². This is because the curve bends upwards or downwards more and more sharply as x increases in absolute value.

As x approaches positive infinity, the term x will become increasingly large and positive. Therefore, the function f(x) will also approach positive infinity. This means that the end behavior of f(x) as x approaches positive infinity is
`$y\rightarrow\infty$`.

Similarly, as x approaches negative infinity, the term x² will become increasingly large, but negative. Therefore, the function f(x) will approach negative infinity. This means that the end behavior of f(x) as x approaches negative infinity is
`$y\rightarrow-\infty$`.

In conclusion, the end behavior of f(x) is
`$y\rightarrow\infty$` as
`$x\rightarrow\infty$` and
`$y\rightarrow-\infty$` as
`$x\rightarrow-\infty$` and the correct option is C.