Question

Select all of the statements that can be determined from the table given.X-4-3-2-10123453f(x)80-6-10-12-12-10-608A. There are x-intercepts at (0, 4) and (0, -3).B. There is a y-intercept at (-12, 0).C. There is a line of symmetry at x = 0.5.D. In the interval from x = -4 to x = 0, F(x) is decreasing.

Answer 1

C. There is a line of symmetry at x = 0.5

D. In the interval from x = -4 to x = 0, F(x) is decreasing

Explanation

At the x-intercept of a function, the value of f(x) is zero. From the table, the x-intercepts are (-3, 0) and (4, 0)

At the y-intercept of a function, the value of the x-variable is zero. From the table, the y-intercept is (0, -12)

The table shows the same equidistant values of f(x) from x = -4 to x = 0 and from x = 1 to x = 5, but following an inverse order. This means that the line of symmetry is placed between x = 0 and x = 1, that is,

`\begin{gathered} \text{ line of symmetry: }x=(0+1)/(2) \\ line\text{ of symmetry: }x=0.5 \end{gathered}`

In the interval from x = -4 to x = 0, the values of f(x) are 8, 0, -6, -10, -12. Each value is less than the previous one, then f(x) is decreasing in this interval