The function g(x) is a translation of f(x) = (x + 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which
function could be g(x)?
g(x) = (x – 2)2 + k
g(x) = (x + 8)2 + k
g(x) = (x – h)2 – 5
g(x) = (x – h)2 – 15
g(x) = (x – 2)2 + k
g(x) = (x + 8)2 + k
g(x) = (x – h)2 – 5
g(x) = (x – h)2 – 15
2 answers:
The function provided is:
f(x)= (x+3)² - 10
We need to determine g(x), which is shifted 5 units to the right of f(x).
Firstly, by sketching the graph of f(x) using Desmos,[TAG_12]]
the shape of f(x) appears as a parabola with the vertex at (-3,-10).
The axis of symmetry is the line that bisects the parabola into two symmetrical halves.
Thus, the equation for g(x) can be expressed as g(x)= (x+3-5)² + K →→→[∵ The axis of symmetry of g(x) moves 5 units to the right compared to f(x)]
g(x) = (x-2)² + K, →→→→→ -∞≤ k≤∞
Setting K= -10 results in g(x)=(x-2)² -10, with the graphs of both f(x) and g(x) displayed below.
Option (A), g(x) = (x-2)² + K, →→→→→ -∞≤ k≤∞ is the correct selection.
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Answer:
The Mean Absolute Deviation (MAD) for her dataset is 4.
Detailed explanation:
Vivian collected data from local cyclists to find the typical miles they rode daily.
Her recorded figures are shown below:
7, 10, 13, 4, 12, 21, 10, 3
= 10
Data point Distance from mean
1 7 7 - 10 = | -3 | = 3
2. 10 10 - 10 = | 0 | = 0
3. 13 13 - 10 = | 3 | = 3
4. 4 4 - 10 = | -6 | = 6
5. 12 12 - 10 = | 2 | = 2
6. 21 21 - 10 = | 11 | = 11
7. 10 10 - 10 = | 0 | = 0
8. 3 3 - 10 = | -7 | = 7
Calculating the total distance gives us 3 + 0 + 3 + 6 + 2 + 11 + 0 + 7 = 32
Thus, MAD = = 4
The Mean Absolute Deviation of this data reflects an average variation of 4 miles that cyclists ride daily.