Topic 3 Unit Test: Polynomial Functions (ATA Unit 5)

3

Simplify the expression below. Give your answer in standard form (decreasing order of the exponent with the first alphapatic base variable)

3

Simplify the expression below. Give your answer in standard form (decreasing order of the exponent with the first alphapatic base variable)

3

Simplify the expression below. Give your answer in standard form (decreasing order of the exponent with the first alphapatic base variable)

1

If an even-degree polynomial function has a positive leading coeeficient, which graph could represent this function

Below is the graph of the function f(x)=x^{3}+12x^2+45x+50 . Use these to answer questions 5 to on the right:

1

Domain:

1

2

Match zeros and their multipicity, to the effect of bounces or intersects on the graph for the function below: (note, there is one un-matched item in the column to the right)
f\left(x\right)=2x\left(x+4\right)^6\left(3x-2\right)^3

Draggable item		Corresponding Item
Zero:\frac{2}{3}, multiplicity: 3		intersect
Zero: -4; multiplicity: 6		bounce
		intersect
Zero: 0; multiplicity: 1		bounce

Factor the polynomial completely. (Stop at real factors).

3

50x^{5}-18x

3

x^{4}+216x (there are at 3 real factors)

3

14x^{3}-49x^{2}+21x

3

Solve 3 of the next 4,( in questions 18 to 21) equations by factoring. Simplify all irrational and complex solutions.

4

8x^{3}-98x=0

4

x^{4}-5x^{2}=3x^{2}+48

3

3x^{3}+4x^{2}=12x+16

4

80x^{4}=10x

3

OPTIONAL: Which of the following represent the solutions to the equation f\left(x\right)=x^3+64? Check all that apply.

3

Find the Quotient of \left(w^3+3w^2-31w-26\right)\div \left(w+7\right)

3

OPTIONAL: Find the quotient of
\left(5y^4-23y^3+24y^2-7\right)\div \left(y-3\right)

Use 
f(x)=x^{2}-x,
g(x)=9-2x, and
h(x)=x^{2}+2x-63 
for questions 25 to 30. Select  a minimum of 3 of the 6 questions to do.

2

Find (f+h)(x)

2

3

Evaluate (g \circ h)(-1)

2

Topic 3 Unit Test: Polynomial Functions (ATA Unit 5)

Simplify the expression below. Give your answer in standard form (decreasing order of the exponent with the first alphapatic base variable)

Simplify the expression below. Give your answer in standard form (decreasing order of the exponent with the first alphapatic base variable)

Simplify the expression below. Give your answer in standard form (decreasing order of the exponent with the first alphapatic base variable)

If an even-degree polynomial function has a positive leading coeeficient, which graph could represent this function

Domain:

Match zeros and their multipicity, to the effect of bounces or intersects on the graph for the function below: (note, there is one un-matched item in the column to the right)f\left(x\right)=2x\left(x+4\right)^6\left(3x-2\right)^3

50x^{5}-18x

x^{4}+216x (there are at 3 real factors)

14x^{3}-49x^{2}+21x

8x^{3}-98x=0

x^{4}-5x^{2}=3x^{2}+48

3x^{3}+4x^{2}=12x+16

80x^{4}=10x

OPTIONAL: Which of the following represent the solutions to the equation f\left(x\right)=x^3+64? Check all that apply.

Find the Quotient of \left(w^3+3w^2-31w-26\right)\div \left(w+7\right)

OPTIONAL: Find the quotient of \left(5y^4-23y^3+24y^2-7\right)\div \left(y-3\right)

Find (f+h)(x)

Evaluate (g \circ h)(-1)

Simplify the expression below. Give your answer in standard form (decreasing order of the exponent with the first alphapatic base variable)

Simplify the expression below. Give your answer in standard form (decreasing order of the exponent with the first alphapatic base variable)

Simplify the expression below. Give your answer in standard form (decreasing order of the exponent with the first alphapatic base variable)

If an even-degree polynomial function has a positive leading coeeficient, which graph could represent this function

Domain:

Range:

Relative Mininum:(s)

Relative Maximum(s)

End Behaviour:As x\rightarrow \infty ,\ f\left(x\right)\rightarrow \ ?

End Behaviour: As x\rightarrow- \infty ,\ f\left(x\right)\rightarrow \ ?

Zeros

During which Intervals is the function to the right ONLY increasing? Check all that apply.

Match zeros and their multipicity, to the effect of bounces or intersects on the graph for the function below: (note, there is one un-matched item in the column to the right)f\left(x\right)=2x\left(x+4\right)^6\left(3x-2\right)^3

50x^{5}-18x

x^{4}+216x (there are at 3 real factors)

14x^{3}-49x^{2}+21x

x^{3}-5x^{2}-x+5

8x^{3}-98x=0

x^{4}-5x^{2}=3x^{2}+48

3x^{3}+4x^{2}=12x+16

80x^{4}=10x

OPTIONAL: Which of the following represent the solutions to the equation f\left(x\right)=x^3+64? Check all that apply.

Find the Quotient of \left(w^3+3w^2-31w-26\right)\div \left(w+7\right)

OPTIONAL: Find the quotient of \left(5y^4-23y^3+24y^2-7\right)\div \left(y-3\right)

Find (f+h)(x)

Find \left(g\cdot f\right)\left(x\right)

Find \left(f\circ g\right)\left(x\right)

Evalulate (h-g)(4)

Evaluate (g \circ h)(-1)

The domain of the function below is 'all real numbers' except for which answer \left(\frac{g}{h}\right)\left(x\right)

Range:

Relative Mininum:(s)

Relative Maximum(s)

End Behaviour:As x\rightarrow \infty ,\ f\left(x\right)\rightarrow \ ?

End Behaviour: As x\rightarrow- \infty ,\ f\left(x\right)\rightarrow \ ?

Zeros

During which Intervals is the function to the right ONLY increasing? Check all that apply.

x^{3}-5x^{2}-x+5

Find \left(g\cdot f\right)\left(x\right)

Find \left(f\circ g\right)\left(x\right)

Evalulate (h-g)(4)

The domain of the function below is 'all real numbers' except for which answer \left(\frac{g}{h}\right)\left(x\right)

Match zeros and their multipicity, to the effect of bounces or intersects on the graph for the function below: (note, there is one un-matched item in the column to the right)
f\left(x\right)=2x\left(x+4\right)^6\left(3x-2\right)^3

OPTIONAL: Find the quotient of
\left(5y^4-23y^3+24y^2-7\right)\div \left(y-3\right)

End Behaviour:
As x\rightarrow \infty ,\ f\left(x\right)\rightarrow \ ?

Match zeros and their multipicity, to the effect of bounces or intersects on the graph for the function below: (note, there is one un-matched item in the column to the right)
f\left(x\right)=2x\left(x+4\right)^6\left(3x-2\right)^3

OPTIONAL: Find the quotient of
\left(5y^4-23y^3+24y^2-7\right)\div \left(y-3\right)

End Behaviour:
As x\rightarrow \infty ,\ f\left(x\right)\rightarrow \ ?