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sdas [7]
3 years ago
6

The graph of F(X), shown below, has the same shape as the graph of

Mathematics
1 answer:
marshall27 [118]3 years ago
3 0

Answer:

The correct option is;

D. F(x) = x⁴ - x² + 2

Step-by-step explanation:

From the graph, we have;

The y-intercept =  2, therefore, when x = 0, y = 2

The graph has no x-intercept, therefore, the unction has complex roots

The possible function is F(x) = x⁴ + x² + 2 and F(x) = 2 - x⁴ - x²

The roots of the function, F(x) = x⁴ - x² + 2, is given as follows;

0 = x⁴ - x² + 2

x = (1 ± √(1 - 8))/(2) = (1 ± √(-7))/(2) which are imaginary roots

For F(x) = 2 - x⁴ - x², we have;

0 = 2 - x⁴ - x²

x = (1 ± √(1 + 8))/(2) = (1 ± 3)/(2)

x = 2 or x = -1, therefore, the function, F(x) = 2 - x⁴ - x², has real roots and the only possible solution is F(x) = x⁴ + x² + 2

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worty [1.4K]
The cost of each Piano Lesson = $30
If there are x lessons, the total cost of lessons can be expressed as 30x.

Since the number of lessons cannot be negative, the value of x can be 0 or greater than 0, where x=0 shows no lesson.

For 1 lesson, x = 1
So the cost will be = 30(1) = $30
In ordered pair we can write it as (1, 30)

If we consider there is an option to attend half portion of a lecture, then for 1 and half lectures, x = 1.5
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In ordered pair we can write it as (1.5, 45)

For 3 lesson, x = 3
The cost of 3 lessons will be = $90
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So, from the given options, only following 2 ordered pairs satisfy the given conditions:
1) (1,30)
2) (3, 90)
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