Q: Determine the end behavior of $$f(x) = -2x^5$ + 7x^3$ - x. $$What happens as $$x \to \infty$$ and $$x \to -\infty$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Q: Which of the following is the correct end behavior for $$f(x) = 7x^3$ - 2x^2$ + 1$$?

As $$x \to \infty$$, $$f(x) \to \infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following functions is NOT a polynomial function?

Accepted Answer

$$f(x) = x$$^{1/2}$$ + 2x$$

Question 2

Given $$f(x) = 6x^3$ + 3x^2$ + 5x + 4$$, what is the degree and leading coefficient of the polynomial?

Accepted Answer

Degree: $$3$$, Leading Coefficient: $$6$$

Question 3

Which graph best represents a polynomial function?

Accepted Answer

A graph that is smooth and continuous

Question 4

Determine the end behavior of $$f(x) = -2x^5$ + 7x^3$ - x. $$What happens as $$x 	o \infty$$ and $$x 	o -\infty$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 5

For the polynomial $$f(x) = x^2$(x-3)^2(x+4$$)$$, what is the multiplicity of each zero and does the graph touch or cross the x$-axis at each?

Accepted Answer

At $$x=0$$: multiplicity $$2$$, touch; $$x=3$$: multiplicity $$2$$, touch; $$x=-4$$: multiplicity $$1$$, cross

Question 6

What is the maximum number of turning points for the polynomial $$f(x) = 4x^5$ - 2x^3$ + x$$?

Accepted Answer

$$4$$

Question 7

A chemical reaction rate is modeled by $$R(t) = -t^4$ + 2t^2$ - 5. $$What is the end behavior of $$R(t) as$$ $$t 	o \infty$$?

Accepted Answer

$$R(t) 	o -\infty$$

Question 8

Which of the following is the standard form of the polynomial $$f(x) = 2x + x^3$ - 5$$?

Accepted Answer

$$f(x) = x^3$ + 2x - 5$$

Question 9

A polynomial $$f(x)$$ has zeros at $$x = 1 ($$multiplicity 2) and $$x = -3 ($$multiplicity 1). Which statement is true about the graph at these zeros?

Accepted Answer

At $$x=1$$, the graph touches the $$x-$$axis; at $$x=-3$$, it crosses

Question 10

If $$f(x) = 3x^4$ - 2x^2$ + 7$$, what is the degree, leading coefficient, and maximum number of turning points?

Accepted Answer

Degree: $$4$$, Leading Coefficient: $$3$$, Max turning points: $$3$$

Question 11

Which of the following describes the end behavior of $$f(x) = -x^6$ + 2x^2$ - 1$$?

Accepted Answer

Both ends fall

Question 12

A medical dosage model is given by $$D(x) = 5x^3$ - 2x^2$ + x. $$How many turning points can its graph have at most?

Accepted Answer

$$2$$

Question 13

Which of the following is a true statement about the graph of a polynomial function?

Accepted Answer

It is always smooth and continuous

Question 14

Given $$f(x) = x^2$(x-2)^3$$, what is the behavior of the graph at $$x=2$?

Accepted Answer

The graph crosses the $$x-$$axis

Question 15

Which of the following is the correct end behavior for $$f(x) = 7x^3$ - 2x^2$ + 1$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 16

A polynomial $$f(x)$$ has degree $$n. $$What is the maximum number of turning points it can have?

Accepted Answer

$$n-1$$

Question 17

If $$f(x) = x^4$ - 2x^2$ + 1$$, which of the following is true about its zeros?

Accepted Answer

Some zeros may have multiplicity greater than 1

Question 18

Which of the following functions could model the height of a projectile over time, assuming only gravity acts and no air resistance?

Accepted Answer

$$h(t) = -4.9t^2$ + v_0t + h_0$

Question 19

Given $$f(x) = 2x^4$ - 8x^2$ + 6$$, what is the degree, leading coefficient, and end behavior?

Accepted Answer

Degree: $$4$$, Leading Coefficient: $$2$$, Both ends rise

Polynomial Functions: Structure, Graphs, Zeros, and Turning Points

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