Question

X. F(x)

-2 6
-1 0
0 -4
1 -6
3 -4
4 0
5 6
Select all statements that can be determined from table.
A. There is a line symmetry at x=1.5
B. There is a y-intercept at (-4,0)
C. In the interval from x=0 to c=5, F(x) is increasing.
D.
There are x- intercepts at (-1,0) and (4,0)

Answer 1

• A. There is a line symmetry at x=1.5
• D. There are x- intercepts at (-1,0) and (4,0)

Explanation:

The average of x-coordinates corresponding to the same F(x) value is 1.5. That is ...

(-2+5)/2 = (-1+4)/2 = (0+3)/2 = 1.5

The values in the table appear to be symmetrical about x=1.5, so that is a line of symmetry.

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The x-intercept points are those points where F(x) = 0: (-1, 0) and (4, 0).

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The y-intercept is (0, -4), not (-4, 0).

On the interval [0, 5] the function is both decreasing and increasing.