The shape of f(x) = √ x, but shifted nine units to the left and then reflected in both the x-axis and the y-axis
1 answer:
Answer:
g(x) = -√(-x +9)
Step-by-step explanation:
The relevant transformations are ...
- f(x -h) . . . . . shifts the graph of f(x) right h units
- f(x) +k . . . . . shifts the graph of f(x) up k units
- -f(x) . . . . . . . reflects the graph of f(x) over the x-axis
- f(-x) . . . . . . . reflects the graph of f(x) over the y-axis
Applying the transformations in the specified order, we have ...
f(x) = √x
f(x +9) = √(x +9) . . . . . . . shifted 9 units to the left
-f(x +9) = -√(x +9) . . . . . . shifted 9 left, reflected in the x-axis
-f(-x +9) = -√(-x +9) . . . . shifted 9 left, reflected in x-axis, reflected in y-axis
The shifted, reflected function is ...
g(x) = -√(-x +9)
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<em>Additional comment</em>
The graph shows the original f(x) = √x function in red. The shifted, reflected function is shown in blue. Note that the initial left shift changes appearance to a right shift when it is reflected over the y-axis.
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Step-by-step explanation:
1.) The equation for the line of least squares regression is given by
where Y = Output Variable = Average Cost (in thousands of dollars)
X = Input Variable = Number of years after 2000
Thus, the given data table transforms as follows:
No. of years after 3 4 5 6 7 8 9 10
after 2000 (X)
Average Cost (Y) 15.505 16.510 17.451 18.471 19.363 20.409 21.093 22.092
To determine the equation precisely, we need to calculate the values of 'm' (Slope) and 'c' (Y-intercept)
Let us take any two random values of X and Y from the above table, so that we have
X₁ = 3; Y₁ = 15.505 and X₂ = 8; Y₂ = 20.409
Plugging in these two sets of values, we get the following two equations:
15.505 = (3)m + c and
20.409 = (8)m + c
Let us subtract the upper one from the lower one so that we have
20.409 - 15.505 = 8m + c - 3m - c
4.904 = 5m
Hence, m = 0.9808
Using this value and plugging it in one of the above equations yields the value of c as
20.409 = 8(0.9808) + c
Therefore, c = 12.563
So, the required equation for the line of least squares regression is
Y = (0.9808)X + 12.563
2.) To estimate the cost of tuition at a 4-year institution in 2000, we can put the value of X to be 0.
We have Y = 0 + 12.563
Thus, the cost of tuition in 2000 was $12,563.
3.) To estimate the cost of tuition in 2020, we put the value of X as 20 so that we have
Y = (0.9808)(20) + 12.563 = 32.179
Therefore, we can expect the cost of tuition to be as high as $32,179 by 2020.
4.) The slope tells us the factor by which the tuition increases each year, starting with the base of 12,563 dollars in 2000.
One way to lower the cost of college tuition is by applying for a waiver based on income level. Alternatively, one can also work at the school.
One can join a part-time graduation program while working for the rest of the day so that one may support oneself as well as pay for their courses. Alternatively, one can opt for Online Courses and get some Diploma in their area of interest while working part-times so that they may pursue a degree later on in their life.
The correct statement is D.
Step-by-step explanation:
Given,
For backyard
Length = 5x-2
Width = 2x+4
For house
Length = 5x-2
Width = 4x-12
For driveway
Length = x+10
Width = 4x-12
To find the correct statement.
Formula
The area of a rectangle = Length × Width
So,
The area of the house and the driveway = (5x-2)(4x-12) + (x+10)(4x-12)
= (4x-12)(5x-2+x+10)
= (4x-12)(6x+8)
=
=
So, the correct statement is D
You can cross check the other statements.