Question

[Algebra 2 / 24 POINTS] Increasing/decreasing functions. Picture included.

1. The function is ______ for –9 < x < –7.
a. increasing
b. decreasing
c. constant

2. The function is increasing for...
a. -3 < x < 0
b. -7 < x < -3
c. -9 < x < -7

3. The point _____ lies on the graph of the function.
a. (-5,8)
b. (-5,-8)
c. (5, -8)

Thank you so much.

Answer 1

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Explanation:

Answer 2

A function f(x) is said to be increasing and Decreasing, if for any two x values ,
`x_(1) ,\text{and},x_(2)`

If,

`x_(1) >x_(2)\\\\ \text{then}\\\\ f(x_(1)) >f(x_(2))`

And ,said to be decreasing , if

`x_(1) >x_(2)\\\\ \text{then}\\\\ f(x_(1)) <f(x_(2))`

And ,Constant function , if it is Neither increasing function nor Decreasing function.

→It is given that, the function is an even function.So, graph will be Symmetrical in first and Second Quadrant.

→If you will look in first Quadrant, in the Interval (7,9) the even function is Constant.

So, the function will be, Constant, in the interval , -9<x<-7.

Option C

2.⇒The function is increasing in the interval

-7<x<-3

Option B: -7 < x < -3

3.⇒Point (5,8) lies on the graph of the function.

So, Point (-5,8) will also lie on the graph of the function.

Option A: (-5,8)