Which statements about the graph of the function f(x) = –x2 – 4x 2 are true? check all that apply.

1.the domain is {x|x ≤ –2}.

2.the range is {y|y ≤ 6}.

3. the function is increasing over the interval (–∞ , –2).

4.the function is decreasing over the interval (−4, ∞).

5.the function has a positive y-intercept.

we have that

using a graph tool

see the attached figure

Statements

case a) The domain is {x|x ≤ –2}-------> Is False

the domain is all real numbers---------> the interval solution is (-∞,∞)

case b) The range is {y|y ≤ 6}.------> Is True

The range is the interval (-∞,6]

case c) The function is increasing over the interval (–∞ , –2).-----> Is True

See the attached figure

case d) The function is decreasing over the interval (−4, ∞).-----> Is False

In the interval (-4,-2) the function is increasing and in the interval (-2,∞) the function is decreasing (See the attached figure)

case e) The function has a positive y-intercept.------> Is True

The value of y-intercept is

therefore

the answer is

The range is {y|y ≤ 6}

The function is increasing over the interval (–∞ , –2)

The function has a positive y-intercept

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.