Answer:
- C. It has 4 zeros and at most 3 relative maximums or minimums.
- D. Both ends of the graph of the function go up.
- F. It is a translation of the parent function 4 units to the right.
Explanation:
You want the statements that describe the function f(x) = 2(x -4)⁴.
Degree
The degree of the function is the exponent: 4. This means the function has 4 zeros.
The maximum number of relative extrema is 1 less than the degree. The function has at most 3 relative maximums or minimums.
The even degree means both ends of the graph go in the same direction.
Leading coefficient
The leading coefficient of 2 is positive, so the ends of the function will go up.
Horizontal translation
In the parent function f(x) = x⁴, the value of x has been replaced by (x-4). This causes the graph to be translated 4 units to the right.
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Additional comment
This function has a zero at (4, 0) with multiplicity 4. There is a flat spot where the graph touches, but does not cross, the x-axis. As a consequence, there is only one minimum and no relative maximums.
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