Math12 1 Transformations 1

1. The polynomial function P(x) = x(x+1)(x+2) has three zeros: 0, -1, -2. What are the zeros of $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»p«/mi»«mfenced»«mrow»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mi»x«/mi»«/mrow»«/mfenced»«/math»$ ?

0, -1, -2

0, -4, -8

0, -1/4, -1/2

0, 1, 2

The given polynomial function P(x) = x(x+1)(x+2) has three zeros: 0, -1, and -2. The zeros of a polynomial are the values of x for which the function equals zero. In this case, when x = 0, x+1 = 0, and x+2 = 0, the function equals zero. Therefore, the zeros of the function are 0, -1, and -2. The answer choice 0, -4, -8 does not match the zeros of the function, so it is not correct. The answer choice 0, -1/4, -1/2 also does not match the zeros of the function. The answer choice 0, 1, 2 also does not match the zeros of the function.

Explanation

The given polynomial function P(x) = x(x+1)(x+2) has three zeros: 0, -1, and -2. The zeros of a polynomial are the values of x for which the function equals zero. In this case, when x = 0, x+1 = 0, and x+2 = 0, the function equals zero. Therefore, the zeros of the function are 0, -1, and -2. The answer choice 0, -4, -8 does not match the zeros of the function, so it is not correct. The answer choice 0, -1/4, -1/2 also does not match the zeros of the function. The answer choice 0, 1, 2 also does not match the zeros of the function.

2. The polynomial function P(x) = x(x+1)(x+2) has three zeros: 0, -1, -2. What are the zeros of y= -2P(x)?

0, 2, 4

0, 1/2, 1

0, -2, -4

0, -1, -2

The zeros of a polynomial function are the values of x for which the function equals zero. In this case, the polynomial function P(x) = x(x+1)(x+2) has zeros at x = 0, x = -1, and x = -2. When we multiply the function by -2, the zeros remain the same. Therefore, the zeros of y = -2P(x) are also 0, -1, and -2.

Explanation

The zeros of a polynomial function are the values of x for which the function equals zero. In this case, the polynomial function P(x) = x(x+1)(x+2) has zeros at x = 0, x = -1, and x = -2. When we multiply the function by -2, the zeros remain the same. Therefore, the zeros of y = -2P(x) are also 0, -1, and -2.

3. If (8,-6) is a point on the graph of y=f(x), what must be the point on the graph of y= -f(2x)+3? (write your answer in the form of (x,y))

If (8,-6) is a point on the graph of y=f(x), it means that when x=8, y=-6.
To find the point on the graph of y= -f(2x)+3, we need to substitute x=4 into the equation.
When x=4, 2x=8, so we can use the point (8,-6) on the graph of y=f(x).
Plugging in 8 for x, we get y= -f(8)+3. Since y=-6 when x=8, we have y= -(-6)+3=9.
Therefore, the point on the graph of y= -f(2x)+3 is (4,9).

Explanation

If (8,-6) is a point on the graph of y=f(x), it means that when x=8, y=-6.
To find the point on the graph of y= -f(2x)+3, we need to substitute x=4 into the equation.
When x=4, 2x=8, so we can use the point (8,-6) on the graph of y=f(x).
Plugging in 8 for x, we get y= -f(8)+3. Since y=-6 when x=8, we have y= -(-6)+3=9.
Therefore, the point on the graph of y= -f(2x)+3 is (4,9).

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