1)
i) Reflection about y axis i.e. x=0
ii) Horizontal shrink by scale factor 4
iii) vertical shift by 4 units up.
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2) f(x) passes through (1,-1) and (0,1)
So slope = (1+1)/(0-1) = -2
Using point slope form equation of f(x) is
y-1 = -2 (x-0) or y = -2x+1
g(x) passes through (0,-1) and (1,1)
Slope = (2/1) = 2
So using point slope form g(x) is
y-1=2x
Hence we find that y-1 = -2x is transformed into y-1 = 2x
i.e. there is a reflection of f(x) on the line y =1
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Answer:
1.) up
2.) (-2,-5)
3.) x = -2
4.) (-2,-5)
5.) y = -5
6.) -∞ < x < ∞
7.) -5 < y < ∞
8.) (0,0)
9.) (0,0) and (-4,0)
10.) two solutions
Step-by-step explanation:
1.) because the parabola opens upward and the vertex is down
2.) the lowest point of the parabola is (-2,-5)
3.) If a line was drawn through the point x = -2, the two halves of the parabola would look symmetrical ( the same on both sides).
4.) The minimum point on the graph is ( -2,-5), because that is the lowest point on this upward parabola, and we can not determine the maximum.
5.) The minimum value of y is y = -5, because that is the lowest value of y on this graph, and we can not determine the maximum.
6.) Because the arms of the parabola continue traveling through negative infinity and positive infinity on the x-axis, the domain is -∞ < x < ∞.
7.) The arms of the parabola go from y = -5 to infinity, so the range of the parabola is -5 < y < ∞.
8.) The parabola first crosses the y-axis at the point (0,0)
9.) The parabola first crosses the x-axis at the points (0,0) and (-4,0)
10,) The solution to the parabola is the variable x. The solutions (x intercepts) of the parabola are x = 0 and x = -4.
Does this help you?
Answer:
scale factor (k) is 2
Step-by-step explanation:
Look at W and W'. W is (-2, -1), but W' says (-4, -2). 2 x 2 is 4 and 1 x 2 is 2. Both coordinates were multiplied by 2. The same goes for all the other vertices, so it would be k = 2.
Answer:
Infinitely Many Solutions
Step-by-step explanation:
Given
![\left[\begin{array}{cccccc}1&2&3&4&5&6\\7&6&5&4&3&2\\8&8&8&8&8&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccccc%7D1%262%263%264%265%266%5C%5C7%266%265%264%263%262%5C%5C8%268%268%268%268%268%5Cend%7Barray%7D%5Cright%5D)
Required
Determine the type of solution
From the matrix, we have:
3 non-zero rows and 5 variables (the last column is the result)
When the number of variables is more than the number of non-zero rows, then such system has infinitely many solutions
i.e.
![Variables > Non\ zero\ rows](https://tex.z-dn.net/?f=Variables%20%3E%20Non%5C%20zero%5C%20rows)
![5 > 3](https://tex.z-dn.net/?f=5%20%3E%203)