SOLUTION: What is the x- and y- axis of f(x)=(x-4)(x+2)^2(x-2) Also, does the graoh of f touch or cross the x-axis at the x-intercept?

Question 821326: What is the x- and y- axis of f(x)=(x-4)(x+2)^2(x-2)
Also, does the graoh of f touch or cross the x-axis at the x-intercept?
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Read the zeros directly from the function definition and use them as critical points which define intervals along the x-axis.
The zeros are at -2, 2, and 4. You want to check a value for sign in each of the intervals:
;
;
;
.

Intuitively, you would well guess that f(x) will be positive in and in .

Try 0 within :
, so positive.

Try 3 within :
, negative.

You should sketch a graph based on these and you then can find where f touches or crosses the x-axis. Note what happens around ; positive on both sides near this, so f not cross the x-axis, but TOUCHES it only.

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