Exam 3: Polynomial and Rational Functions

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 4 + 5 x + x ^ { 2 }$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 4 + 5 x + x ^ { 2 }$

(Multiple Choice)

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Question 161

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4$

(Multiple Choice)

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Question 162

Find the degree of the polynomial function. - $f ( x ) = 18 x ^ { 5 } + 4 x ^ { 4 } - 9$

(Multiple Choice)

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Question 163

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $x ^ { 5 } - 14 x ^ { 3 } + 45 x = 0$

(Multiple Choice)

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Question 164

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = ( x + 1 ) ^ { 2 } - 1$

(Multiple Choice)

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Question 165

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - $f ( x ) = 6 x ^ { 5 } - 7 x ^ { 3 } + 6 x ^ { 2 } - 2$ ; between $- 2$ and $- 1$

(Multiple Choice)

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Question 166

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 36$

(Multiple Choice)

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Question 167

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = x ^ { 3 } - 4 x$

(Multiple Choice)

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Question 168

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $( x ) = 4 x ^ { 4 } + 4 x ^ { 3 } + 4 x ^ { 2 } + 5 x + 3$

(Multiple Choice)

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Question 169

Solve the problem -The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 400$ . Find the number of pretzels that must be sold to maximize profit.

(Multiple Choice)

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Question 170

Find the y-intercept of the polynomial function. - $f ( x ) = 7 x - x ^ { 3 }$

(Multiple Choice)

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Question 171

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - $f ( x ) = 5 x ^ { 3 } - 7 x + 7$ ; between $- 2$ and $- 1$

(Multiple Choice)

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Question 172

The graph of a quadratic function is given. Determine the function's equation. -

(Multiple Choice)

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Question 173

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$

(Multiple Choice)

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Question 174

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. -

(Multiple Choice)

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Question 175

The graph of a quadratic function is given. Determine the function's equation. -

(Multiple Choice)

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Question 176

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = ( x + 1 ) ^ { 2 } - 1$

(Multiple Choice)

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Question 177

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = ( x + 3 ) ( x + 4 ) ( x + 5 ) ^ { 2 }$

(Multiple Choice)

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Question 178

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 1$

(Multiple Choice)

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Question 179

Find the degree of the polynomial function. - $- 15 x ^ { 3 } - 7 x ^ { 2 } - 8 x + 2 y ^ { 4 } - 5$

(Multiple Choice)

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Question 180

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 4 + 5 x + x ^ { 2 }$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 4 + 5 x + x ^ { 2 }$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4$

Find the degree of the polynomial function. - $f ( x ) = 18 x ^ { 5 } + 4 x ^ { 4 } - 9$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $x ^ { 5 } - 14 x ^ { 3 } + 45 x = 0$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = ( x + 1 ) ^ { 2 } - 1$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - $f ( x ) = 6 x ^ { 5 } - 7 x ^ { 3 } + 6 x ^ { 2 } - 2$ ; between $- 2$ and $- 1$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 36$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = x ^ { 3 } - 4 x$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $( x ) = 4 x ^ { 4 } + 4 x ^ { 3 } + 4 x ^ { 2 } + 5 x + 3$

Solve the problem -The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 400$ . Find the number of pretzels that must be sold to maximize profit.

Find the y-intercept of the polynomial function. - $f ( x ) = 7 x - x ^ { 3 }$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - $f ( x ) = 5 x ^ { 3 } - 7 x + 7$ ; between $- 2$ and $- 1$

The graph of a quadratic function is given. Determine the function's equation. -

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. -

The graph of a quadratic function is given. Determine the function's equation. -

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = ( x + 1 ) ^ { 2 } - 1$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = ( x + 3 ) ( x + 4 ) ( x + 5 ) ^ { 2 }$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 1$

Find the degree of the polynomial function. - $- 15 x ^ { 3 } - 7 x ^ { 2 } - 8 x + 2 y ^ { 4 } - 5$

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Exam 3: Polynomial and Rational Functions

Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=4+5x+x2f ( x ) = 4 + 5 x + x ^ { 2 }f(x)=4+5x+x2

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - f(x)=x3+4x2−x−4f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4f(x)=x3+4x2−x−4

Find the degree of the polynomial function. - f(x)=18x5+4x4−9f ( x ) = 18 x ^ { 5 } + 4 x ^ { 4 } - 9f(x)=18x5+4x4−9

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - x5−14x3+45x=0x ^ { 5 } - 14 x ^ { 3 } + 45 x = 0x5−14x3+45x=0

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=(x+1)2−1f ( x ) = ( x + 1 ) ^ { 2 } - 1f(x)=(x+1)2−1

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - f(x)=6x5−7x3+6x2−2f ( x ) = 6 x ^ { 5 } - 7 x ^ { 3 } + 6 x ^ { 2 } - 2f(x)=6x5−7x3+6x2−2 ; between −2- 2−2 and −1- 1−1

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - f(x)=x3+10x2+33x+36f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 36f(x)=x3+10x2+33x+36

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - f(x)=x3−4xf ( x ) = x ^ { 3 } - 4 xf(x)=x3−4x

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - (x)=4x4+4x3+4x2+5x+3( x ) = 4 x ^ { 4 } + 4 x ^ { 3 } + 4 x ^ { 2 } + 5 x + 3(x)=4x4+4x3+4x2+5x+3

Solve the problem -The profit that the vendor makes per day by selling xxx pretzels is given by the function P(x)=−0.004x2+2.4x−400P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 400P(x)=−0.004x2+2.4x−400 . Find the number of pretzels that must be sold to maximize profit.

Find the y-intercept of the polynomial function. - f(x)=7x−x3f ( x ) = 7 x - x ^ { 3 }f(x)=7x−x3

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - f(x)=5x3−7x+7f ( x ) = 5 x ^ { 3 } - 7 x + 7f(x)=5x3−7x+7 ; between −2- 2−2 and −1- 1−1

The graph of a quadratic function is given. Determine the function's equation. -

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - f(x)=(x−2)2(x2−9)f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)f(x)=(x−2)2(x2−9)

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. -

The graph of a quadratic function is given. Determine the function's equation. -

Find the y-intercept for the graph of the quadratic function. - f(x)=(x+1)2−1f ( x ) = ( x + 1 ) ^ { 2 } - 1f(x)=(x+1)2−1

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - f(x)=(x+3)(x+4)(x+5)2f ( x ) = ( x + 3 ) ( x + 4 ) ( x + 5 ) ^ { 2 }f(x)=(x+3)(x+4)(x+5)2

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=x2−1f ( x ) = x ^ { 2 } - 1f(x)=x2−1

Find the degree of the polynomial function. - −15x3−7x2−8x+2y4−5- 15 x ^ { 3 } - 7 x ^ { 2 } - 8 x + 2 y ^ { 4 } - 5−15x3−7x2−8x+2y4−5

Equations and Inequalities

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Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 4 + 5 x + x ^ { 2 }$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 4 + 5 x + x ^ { 2 }$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4$

Find the degree of the polynomial function. - $f ( x ) = 18 x ^ { 5 } + 4 x ^ { 4 } - 9$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $x ^ { 5 } - 14 x ^ { 3 } + 45 x = 0$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = ( x + 1 ) ^ { 2 } - 1$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - $f ( x ) = 6 x ^ { 5 } - 7 x ^ { 3 } + 6 x ^ { 2 } - 2$ ; between $- 2$ and $- 1$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 33 x + 36$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = x ^ { 3 } - 4 x$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $( x ) = 4 x ^ { 4 } + 4 x ^ { 3 } + 4 x ^ { 2 } + 5 x + 3$

Solve the problem -The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 400$ . Find the number of pretzels that must be sold to maximize profit.

Find the y-intercept of the polynomial function. - $f ( x ) = 7 x - x ^ { 3 }$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - $f ( x ) = 5 x ^ { 3 } - 7 x + 7$ ; between $- 2$ and $- 1$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = ( x + 1 ) ^ { 2 } - 1$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = ( x + 3 ) ( x + 4 ) ( x + 5 ) ^ { 2 }$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 1$

Find the degree of the polynomial function. - $- 15 x ^ { 3 } - 7 x ^ { 2 } - 8 x + 2 y ^ { 4 } - 5$