Question

¿cómo hacerlo? encuentra cada característica fundamental. 4. dominio 5. rango 6. intercepto(s) en x 7. intercepto(s) en y 8. intervalo(s) en que la gráfica es positiva 9. intervalo(s) en que la gráfica es decreciente 10. intervalo(s) en que la gráfica es creciente 11. tasa de cambio promedio en -1, 4

Explanation:

Step1: Identify domain from graph

The domain is the set of all x - values for which the function is defined. Looking at the graph, the x - values range from - 4 to 4. So, the domain is $[-4,4]$.

Step2: Identify range from graph

The range is the set of all y - values. The lowest y - value is - 1 and the highest is 3. So, the range is $[-1,3]$.

Step3: Find x - intercepts

The x - intercepts are the points where the graph crosses the x - axis. The graph crosses at $x = 0$ and $x = 4$. So, the x - intercepts are $x = 0$ and $x = 4$.

Step4: Find y - intercepts

The y - intercept is the point where the graph crosses the y - axis. The graph crosses at $y = 0$. So, the y - intercept is $y = 0$.

Step5: Find positive intervals

The graph is positive when $y>0$. This occurs on the intervals $[0,4]$.

Step6: Find decreasing intervals

The graph is decreasing when the slope is negative. This occurs on the intervals $[-4,-2]$ and $[2,4]$.

Step7: Find increasing intervals

The graph is increasing when the slope is positive. This occurs on the intervals $[-2,2]$.

Step8: Calculate average rate of change

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$, $b = 4$. When $x=-1$, $y=-1$ and when $x = 4$, $y = 0$. So the average rate of change is $\frac{0-(-1)}{4-(-1)}=\frac{1}{5}$.

Answer:

1. Domain: $[-4,4]$
2. Range: $[-1,3]$
3. x - intercepts: $x = 0,x = 4$
4. y - intercept: $y = 0$
5. Positive intervals: $[0,4]$
6. Decreasing intervals: $[-4,-2],[2,4]$
7. Increasing intervals: $[-2,2]$
8. Average rate of change on $[-1,4]$: $\frac{1}{5}$