Answer:
The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is 
.
The domain of the function is all real numbers and its range is between -4 and 5.
The graph is enclosed below as attachment.
Step-by-step explanation:
Let be 
the base formula, where 
is measured in sexagesimal degrees. This expression must be transformed by using the following data:
(Period)
(Minimum)
(Maximum)
The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of 
radians. In addition, the following considerations must be taken into account for transformations:
1) must be replaced by 
. (Horizontal scaling)
2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:
3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)
The new function is:
Given that , and , the outcome is:
The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.
Sub in 2 for x and solve for y
x + 3 = y
2 + 3 = y
5 = y
so ur points are : (2,5)
Answer:
Samuel slept for 1/4 of the distance.
Step-by-step explanation:
The information provided are:
- Samuel fell asleep halfway home.
- He didn't wake up until he still had half as far to go as he had already
- gone while asleep.
Consider that the total distance covered was 1.
Then from the first point we know that Samuel fell asleep after covering a distance of 1/2.
It is provided that he woke up only after covering half of the remaining distance.
That is, he slept for 1/4 of the remaining distance.
Thus, Samuel was asleep for 1/4th of the entire trip home.
There seems to be a flaw with this question because it says that there are five x-intercepts but the given information only gives you 4 x-intercepts to work with.
Even means the graph is symmetric about the y-axis
The best answer is <span>A.(–6, 0), (–2, 0), and (0, 0)
because you do not have to worry about another point (0,0). Plus we need (-6,0) for it to be symmetric with (6,0).
Consider function f(x) = x²(x-6)(x+6)(x+2)</span>²(x-2)<span>². It is even and fits these conditions as it has x-intercepts at (6,0), (-6,0), (-2,0), (2,0), and (0,0). again, the question does not tell us the fifth x-intercept, so we need to assume that there is another one that needs to be there...and so (-2,0) must have (2,0) for it to be even as well.</span>
