Question

analyzing tables algebra: concepts and connections ic sem a fears 49:34 based on the table, which best predicts the end behavior of the graph of f(x)? as x → ∞, f(x) → ∞, and as x → −∞, f(x) → −∞. as x → ∞, f(x) → ∞, and as x → −∞, f(x) → ∞. as x → ∞, f(x) → −∞, and as x → −∞, f(x) → −∞. as x → ∞, f(x) → −∞, and as x → −∞, f(x) → ∞. (table: x values -4, -3, -2, -1, 0, 1, 2, 3, 4; f(x) values 18, 0, 0, 3, 0, -3, -6, -9, -18)

Explanation:

Step1: Identify the function type

Observe the relationship between $x$ and $f(x)$:
When $x=-4$, $f(x)=18$; $x=-3$, $f(x)=9$; $x=-2$, $f(x)=6$; $x=-1$, $f(x)=3$; $x=0$, $f(x)=0$; $x=1$, $f(x)=-3$; $x=2$, $f(x)=-6$; $x=3$, $f(x)=-9$; $x=4$, $f(x)=-18$.
The function follows $f(x) = -\frac{9}{2}x$, a linear function with a negative slope $m=-\frac{9}{2}$.

Step2: Determine end behavior

For a linear function $f(x)=mx+b$ where $m<0$:
As $x \to \infty$, $f(x) = -\frac{9}{2}x \to -\infty$.
As $x \to -\infty$, $f(x) = -\frac{9}{2}x \to \infty$.

Answer:

As $x \to \infty, f(x) \to -\infty$, and as $x \to -\infty, f(x) \to \infty$.