Can someone help me with these T.T
1.Which polynomial function would have the end behaviour of as x-> -∞, y= +inf and as x-> ∞, y-> -∞?
a) f(x) = -6x^4 - x^5 + 5x^3 - x^2 - 4x + 9
b)f(x)= 6x^4 + x^5 - 5x^3 + x^2 + 4x - 9
c)f(x) = 3x^2 + x - 11
d)-2x^2 + 4x^3 + x - 7
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2. If the leading coefficient of an odd-degree polynomial function is positive, then the function extends from third quadrant to the first quadrant; that is, as
a) x-> ∞, y-> -∞ and as x-> -∞, y-> ∞
b) x-> -∞ , y-> ∞ and as x-> ∞ , y-> -∞
c)x-> -∞ , y-> -∞ and as x-> ∞, y-> ∞
d) x-> -∞, y-> -∞ and as x-> ∞, y-> -∞
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3. What is the maximum number of turning points that the polynomial function f(x) = 4x^7 + 9x^5 - 3x^4 + 2x^2 - 5?
a) 0
b) 2
c) 3
d) 6
The answer is D, 6?
4. Which equation is a quartic function with zeros at -4, -1, 2, 3?
a) y=(x-4)(x-1)(x+2)(x+3)
b) y=(x-2)(x-3)(x+4)(x+1)
c) y=(x+4)^2(x+1)(x-3)
d) y=(x+4)^2(x+1)^2(x-2)^2(x-3)^2
The answer is b, y=(x-2)(x-3)(x+4)(x+1)
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5. Which of the following statements about the function y=a(k(x-d))^n + c is not true?
a) The value of A represents a vertical stretch/compression.
b)The value of D represents a horizontal translation
c) the value of K represents the maximum or minimum of the function.
d) the value of c represents a vertical translation.
The answer is C
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6. Describe the transformations that were applied to y= x^3 to create y=(3/4(x+3))^3 - 2.
a) Horizontally stretched by a factor 4/3, horizontally translated 3 units to the left and vertically translated 2 units down
b) Horizontally stretched by a factor 4/3, horizontally translated 3 units to the left and vertically translated 2 units down
c) Horizontally stretched by a factor 3, horizontally translated 4/3 units to the left and vertically translated 2 units down
d) Horizontally stretched by a factor 3/4, horizontally translated 2 units to the right and vertically translated 3 units up
The answer is C.
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7. Determine the x-intercepts of the function y= 4(x+7)^3 - 32.
a) 2
b) -5
c) -5,5
d) -2,2
The answer is B, -5.
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1. To determine the end behavior of a polynomial function, we look at the highest degree term. In this case, the highest degree term is x^5. Since the coefficient of this term is positive (+1), as x approaches negative infinity, y will approach positive infinity. And as x approaches positive infinity, y will approach negative infinity.
Therefore, the polynomial function that satisfies these conditions is option b) f(x)= 6x^4 + x^5 - 5x^3 + x^2 + 4x - 9.
2. For an odd-degree polynomial function with a positive leading coefficient, as x approaches negative infinity, y will approach negative infinity. And as x approaches positive infinity, y will also approach positive infinity.
Therefore, the correct answer is a) x-> ∞, y-> -∞ and as x-> -∞, y-> ∞.
3. The number of turning points in a polynomial function is equal to the degree of the polynomial minus 1. In this case, the degree of the polynomial function is 7. Therefore, the maximum number of turning points is 7 - 1 = 6.
Hence, the correct answer is d) 6.
4. To find a quartic function with given zeros, we can use the factored form of the function. The function will be in the form y = (x - r1)(x - r2)(x - r3)(x - r4), where r1, r2, r3, and r4 are the given zeros.
In this case, the given zeros are -4, -1, 2, and 3. Therefore, the correct equation is y = (x - 2)(x - 3)(x + 4)(x + 1).
Thus, the correct answer is b) y = (x - 2)(x - 3)(x + 4)(x + 1).
5. The correct answer is b because the value of K represents the compression or dilation factor, not the maximum or minimum of the function. The value of A represents a vertical stretch/compression, D represents a horizontal translation, and c represents a vertical translation.
6. To describe the transformations applied to y = x^3 to create y = (3/4(x + 3))^3 - 2, we can observe the changes to the original equation. First, the function is horizontally stretched by a factor of 3/4. This is because the coefficient of x is changed from 1 to 3/4. Second, the function is horizontally translated 3 units to the left. This is because the equation is now (x + 3) instead of just x. Finally, the function is vertically translated 2 units down. This is indicated by the -2 at the end of the equation.
Therefore, the correct answer is a) Horizontally stretched by a factor 4/3, horizontally translated 3 units to the left, and vertically translated 2 units down.
7. To find the x-intercepts of a function, we set y equal to zero and solve for x. In this case, we have the equation y = 4(x + 7)^3 - 32. Setting y equal to zero, we get 4(x + 7)^3 - 32 = 0. Simplifying this equation, (x + 7)^3 - 8 = 0. From here, we can solve for x by taking the cube root of both sides and solving for x + 7. By cube rooting both sides, we get x + 7 - 2 = 0. Simplifying this, x + 5 = 0. Solving for x, we get x = -5.
Therefore, the correct answer is b) -5.