What is the minimum number of colors you can use to color each map below using different colors for neighboring regions?
2 answers:
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Answer:
Hence the function which has the smallest minimum is: h(x)
Step-by-step explanation:
We are given function f(x) as:
- f(x) = −4 sin(x − 0.5) + 11
We know that the minimum value attained by the sine function is -1 and the maximum value attained by sine function is 1.
so the function f(x) receives the minimum value when sine function attains the maximum value since the term of sine function is subtracted.
Hence, the minimum value of f(x) is: 11-4=7 ( when sine function is equal to 1)
- Also we are given a table of values for function h(x) as:
x y
−2 14
−1 9
0 6
1 5
2 6
3 9
4 14
Hence, the minimum value attained by h(x) is 5. ( when x=1)
- Also we are given function g(x) ; a quadratic function passing through (2,7),(3,6) and (4,7)
so, the equation will be:
Hence on putting these coordinates we will get:
a=1,b=3 and c=7.
Hence the function g(x) is given as:
So,the minimum value attained by g(x) could be seen from the graph is at the point (3,6).
Hence, the minimum value attained by g(x) is 6.
Hence the function which has the smallest minimum is h(x)
Here the list of the transformations applied to the parent function, and their effect:
. This causes a horizontal compression of factor 4.
. This causes a horizontal translation, 3 units to the left.
. This causes a reflection about the x axis.
. This causes a vertical translation, 3 units up
So, if you start from the graph of , you have to compress and translate it horizontally, flip it with respect to the x axis, and finally move it up 3 units.