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

Last updated almost 3 years ago
30 questions
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

Range:

1

Relative Mininum:(s)

1

Relative Maximum(s)

1

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

1

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

2

Zeros

2

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

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 itemCorresponding Item

intersect
Zero:\frac{2}{3}, multiplicity: 3
bounce
Zero: -4; multiplicity: 6
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

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

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

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

3

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

3

Evalulate (h-g)(4)

3

Evaluate (g \circ h)(-1)

2

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