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klemol [59]
3 years ago
7

Which of the following functions is graphed below??

Mathematics
2 answers:
il63 [147K]3 years ago
6 0

Answer:

The required piece-wise function is

f(x)=\begin{cases}x^3-3 & \text{ if } x\leq 2 \\ x^2+6 & \text{ if } x>2 \end{cases}

Step-by-step explanation:

From the given graph it is clear that it is a piece-wise function because it is braked in two parts.

One part is defined for x≤2 and other part is defined for x>2 because left curve has closed circle at x=2 and right curve has open circle at x=2.

The y-intercept of the function is -3. From the given graph it is clear that the graph defined for x≤2 is a graph of cubic function that shifts 3 units down. So, the required function for x≤2.

f(x)=x^3-3

From the given graph it is clear that the right curve passes through the point (3,15) and moves towards (2,10).

The function f(x)=x^2+6 satisfied by both the points. So, the required function for x>2.

f(x)=x^2+6

Therefore the required piece-wise function is

f(x)=\begin{cases}x^3-3 & \text{ if } x\leq 2 \\ x^2+6 & \text{ if } x>2 \end{cases}

stellarik [79]3 years ago
3 0
It should be B on my opinion
I hope this help you
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