Subjects algebra

Cubic End Behavior 39A979

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1. The problem asks to describe the end behavior of a cubic function graph passing through the origin (0,0). 2. For cubic functions of the form $f(x) = ax^3 + bx^2 + cx + d$, the end behavior depends on the leading term $ax^3$. 3. Since the graph slopes downward to negative values as $x \to -\infty$ and upward to positive values as $x \to \infty$, the leading coefficient $a$ is positive. 4. Therefore, as $x \to \infty$, $f(x) \to \infty$. 5. As $x \to -\infty$, $f(x) \to -\infty$. 6. In summary: - As $x$ approaches infinity, $f(x)$ approaches positive infinity. - As $x$ approaches negative infinity, $f(x)$ approaches negative infinity. This matches the typical end behavior of a cubic function with a positive leading coefficient.