Math

QuestionFind the values of xx where f(x)=0f(x)=0 and f(x)>0f(x)>0 given points: (8,0)(8,0), (4,6)(4,-6), (0,3)(0,-3), (14,6)(-14,-6), (2,0)(-2,0), (4,6)(-4,6), (6,9)(-6,9), (12,0)(-12,0).

Studdy Solution

STEP 1

Assumptions1. The points given are on the graph of the function ff. . The function ff is continuous and well-defined at all the given points.

STEP 2

To find the value(s) of xx for which f(x)=0f(x)=0, we need to look at the points where the y-coordinate is0.

STEP 3

From the given points, we can see that the y-coordinate is0 at the points (8,0)(8,0), (2,0)(-2,0), and (12,0)(-12,0).

STEP 4

Therefore, the values of xx for which f(x)=0f(x)=0 are x=8x=8, x=2x=-2, and x=12x=-12.

STEP 5

To find the values of xx for which f(x)>0f(x)>0, we need to look at the points where the y-coordinate is positive.

STEP 6

From the given points, we can see that the y-coordinate is positive at the points (4,6)(-4,6) and (6,9)(-6,9).

STEP 7

However, we can't just say that f(x)>0f(x)>0 for x=4x=-4 and x=6x=-6. We need to consider the intervals between the points where f(x)=0f(x)=0.

STEP 8

From the given points, we can see that f(x)f(x) changes from negative to positive between the points (2,0)(-2,0) and (4,6)(-4,6), and remains positive up to the point (6,)(-6,).

STEP 9

Then f(x)f(x) changes from positive to negative between the points (6,9)(-6,9) and (12,)(-12,).

STEP 10

Therefore, the values of xx for which f(x)>0f(x)>0 are in the interval (4,2)(-4,-2).
Please note that without the graph or more information about the function, we can't determine if there are other intervals where f(x)>0f(x)>0.

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