Unit Test — Unit test Answers

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What are the possible degrees for the polynomial function?

degrees of 6 or greater

even degrees of 6 or greater

degrees of 5 or greater

odd degrees of 5 or greater

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Which expression is a possible leading term for the polynomial function graphed below?

–4x8

–4x5

4x5

4x8

Carlos graphed the system of equations that can be used to solve .What are the roots of the polynomial equation?

–3, –2, 3

–3, 2

18, 32

18, 32, 66

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

She is incorrect because systems may have only complex solutions which are not visible on a graph.

She is incorrect because the solutions may have multiplicity greater than 1.

She is correct because all solutions are intersection points of the graphs.

She is correct because the solutions are irrational.

A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?

The graph of the function is positive on (–6, –2).

The graph of the function is negative on (, 0).

The graph of the function is positive on (–2, 4).

The graph of the function is negative on (4, ).

What are the solutions of the equation (x – 3)2 + 2(x – 3) – 8 = 0? Use u substitution to solve.

x = –5 and x = 1

x = –1 and x = 5

x = –1 and x = –7

x = 1 and x = 7

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?

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Which equation is quadratic in form?

3x5 + 8x3 + 6 = 0

6x4 + 7x2 – 3 = 0

5x6 + x4 + 12 = 0

x9 + x3 – 10 = 0

The formula for the volume of a cube is V(s) = s3 where s is the side length of the cube. What is the domain and range of this function?

s < 0, V(s) < 0

s > 0, V(s) < 0

s 0

s > 0, V(s) > 0

Which best describes the end behavior of ?

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.

As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.

As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.

Which statement about the simplified binomial expansion of (a – b)n, where a, b and n are positive integers, is true?

All terms of the expansion are positive.

All terms in the expansion are negative.

The first term in the expansion is positive.

The first term in the expansion is negative.

Which expression represents the sixth term in the binomial expansion of (5y + 3)10?

10C5(5y)5(3)5

10C6(5y)4(3)6

510C5(y)5(3)5

510C6(y)4(3)6

Which statement best describes the equation (x + 5)2 + 4(x + 5) + 12 = 0?

The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u = (x + 5).

The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.

The equation is not quadratic in form because it cannot be solved by using the quadratic formula.

The equation is not quadratic in form because there is no real solution.

The formula for the volume of a cylinder with a height of 5 units is where r is the radius of the cylinder. What is the domain and range of this function?

r < 0, V(r) < 0

r > 0, V(r) < 0

r 0

r > 0, V(r) > 0

What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

x = StartFraction negative 4 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction

x = StartFraction negative 7 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction

x = –7 and x = –2

x = –1 and x = 4

Which statement describes the function y = axn when a = 1 and n is odd?

The graph opens down.

The graph is symmetric about the origin.

The graph does not pass through the origin.

The graph has more than one x intercept.

Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?

f(x) = x2(x – a)2(x – b)4(x – c)

f(x) = x3(x – a)3(x – b)(x – c)2

f(x) = x4(x – a)(x – b)3(x – c)3

f(x) = (x – a)2(x – b)(x – c)6

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

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The owner of a coffee shop chain creates a graph representing sales in thousands of dollars. She describes the characteristics as follows:• There have been two turning points in sales this year.• Sales are expected to increase in the long run.• The least amount of sales during the year is about $250,000.Which graph correctly shows the coffee shop’s sales?

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