Question

1. state the maximum height:
2. state the minimum height:
3. state the interval(s) of increasing height (x values)
4. state the interval(s) of decreasing height (x values)
5. what is the rate of change on the interval -4,2

Explanation:

Step1: Determine maximum height

The maximum height is the highest \( y - \) value on the graph. Looking at the graph, the highest \( y - \) value is \( 7\).

Step2: Determine minimum height

The minimum height is the lowest \( y - \) value on the graph. Looking at the graph, the lowest \( y - \) value is \(-3\).

Step3: Find interval of increasing height

A function is increasing when as \( x \) increases, \( y \) increases. From the graph, the function is increasing on the interval \((-1,1)\).

Step4: Find interval of decreasing height

A function is decreasing when as \( x \) increases, \( y \) decreases. From the graph, the function is decreasing on the intervals \((-10,-5)\), \((-5,-1)\) and \((1,10)\).

Step5: Calculate rate of change on \([-4,2]\)

The rate of change formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
When \(x=-4\), \(y=-2\) (approximate value from the graph) and when \(x = 2\), \(y = 7\).
\(m=\frac{7-(-2)}{2-(-4)}=\frac{7 + 2}{2 + 4}=\frac{9}{6}=\frac{3}{2}\)

Answer:

1. \(7\)
2. \(-3\)
3. \((-1,1)\)
4. \((-10,-5)\cup(-5,-1)\cup(1,10)\)
5. \(\frac{3}{2}\)