Question

1. perpendicular to the line y = \frac{1}{7}x + 5, containing the point (2, -3)

a) y = -\frac{1}{7}x - \frac{18}{7} b) y = -7x + 18 c) y = -7x + 19 d) y = 7x - 17

1. perpendicular to the line y = 8, containing the point (1, 8)

a) x = 8 b) x = 1 c) x = 1 d) x = 8

the graph of a function is given. determine whether the function is increasing, decreasing, or constant on the given interval.

1. (-2, \frac{3}{2})

graph of a function with a w - shaped curve
a) increasing b) decreasing c) constant

1. (-2, 0)

graph of a function with a curve having minima and a peak at the origin
a) decreasing b) constant c) increasing

Explanation:

Step1: Analyze the interval \((-2, \frac{3}{2})\) for the first graph

The first graph is a "W"-shaped curve (even - degree polynomial - like). In the interval \((-2,\frac{3}{2})\), we observe the trend of the graph. As we move from left to right (increasing \(x\) - values) in this interval, the \(y\) - values of the graph are decreasing (the graph is going downwards as \(x\) increases in this interval).

Step2: Analyze the interval \((-2,0)\) for the second graph

The second graph has a "M" - shaped (or symmetric with a peak at \(x = 0\)) curve. In the interval \((-2,0)\), as we move from \(x=-2\) to \(x = 0\) (increasing \(x\) - values), the \(y\) - values of the graph are increasing (the graph is going upwards as \(x\) increases in this interval). But since the question for the first graph (109a) is about \((-2,\frac{3}{2})\):

Answer:

For 109a (interval \((-2,\frac{3}{2})\)): B) decreasing

For 109b (interval \((-2,0)\)): C) increasing