The illustration below shows the graph of y as a function of x. Complete the following sentences based on the graph.

Initially, as x increases, y (decreases, increases, or is constant)

Afterward, the slope of the graph of the function is equal to for all x between x=3 and x=5.

The slope of the graph is equal to for x between x=5 and x=9.

The greatest value of y is y=and it occurs when x=

.

1). Increases

2). Slope = 4

3). Slope = -1

4). y = 4 when x = 5

Step-by-step explanation:

1). Initially, as x increases, y also increases. (Linear growth has been shown in the graph initially).

2). Afterward, the slope of the graph of the function is equal to 4 for all x between x = 3 and x = 5.

[Slope of the line passing through two points (3, 0) and (5, 4)

m = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}

(x

2

−x

1

)

(y

2

−y

1

)

= \frac{4-0}{5-3}

5−3

4−0

= \frac{4}{1}

1

4

= 4 ]

3). The slope of the graph is equal to -1 for x between x = 5 and x = 9.

[Slope of the line passing through two points (5, 4) and (9, 0),

Slope = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}

(x

2

−x

1

)

(y

2

−y

1

)

= \frac{4-0}{5-9}

5−9

4−0

= -\frac{4}{4}

4

4

= -1 ]

4). The greatest value of y is y = 4, and it occurs when x = 5. (From the given graph)

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)