Q: Which of the following best describes the end behavior of the polynomial function $$f(x) = -2x^5$ + 3x^3$ - x + 7$$?

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

Q: Which of the following describes the end behavior of $$f(x) = 3x^4$ - 2x^2$ + 1$$?

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

Question 1

Which of the following best describes the end behavior of the polynomial function $$f(x) = -2x^5$ + 3x^3$ - x + 7$$?

Accepted Answer

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

Question 2

Given the polynomial $$f(x) = x^4$ - 5x^2$ + 4$$, which of the following is a correct set of zeros for $$f(x)$$?

Accepted Answer

$$x = 1, x = -1, x = 2, x = -2$$

Question 3

If a polynomial $$f(x)$$ has a zero at $$x = 3$$ with multiplicity 2, what does the graph do at $$x = 3$$?

Accepted Answer

The graph touches the x-axis at $$x = 3$$ and turns around

Question 4

Which of the following statements about the graph of a polynomial function is TRUE?

Accepted Answer

The graph of a polynomial function is always smooth and continuous

Question 5

A cubic polynomial $$f(x)$$ has three real zeros at $$x = -2$$, $$x = 1$$, and $$x = 3. $$Which of the following could be the equation for $$f(x)$$?

Accepted Answer

$$f(x) = (x + 2)(x - 1)(x - 3)$$

Question 6

According to the Intermediate Value Theorem, if $$f(-3) = -10$$ and $$f(-2) = 5$$ for a polynomial $$f(x)$$, what can you conclude?

Accepted Answer

There is a zero of $$f(x)$$ between $$x = -3$$ and $$x = -2$$

Question 7

What is the maximum number of turning points for the polynomial $$f(x) = x^6$ - 2x^4$ + x^2$?

Accepted Answer

5

Question 8

Which of the following describes the end behavior of $$f(x) = 3x^4$ - 2x^2$ + 1$$?

Accepted Answer

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

Question 9

A real-world scenario: The height $$h (in $$meters) of a projectile at time $$t (in $$seconds) is modeled by $$h(t) = -5t^2$ + 20t + 2. $$What is the y-intercept of this function, and what does it represent?

Accepted Answer

The y-intercept is $$2$$, representing the initial height of the projectile

Question 10

If $$f(x) = x^3$ - 4x^2$ + 4x$$, what are the multiplicities of its zeros?

Accepted Answer

$$x = 0 ($$multiplicity 1), $$x = 2 ($$multiplicity 2)

Question 11

Which of the following is NOT a characteristic of the graph of a polynomial function?

Accepted Answer

It can have sharp corners

Question 12

Suppose $$f(x) = 2(x + 1)^3$(x - 2)^2$. How does the graph behave at x = -1$ and x = 2$?

Accepted Answer

At $$x = -1$$, the graph crosses the x-axis; at $$x = 2$$, the graph touches and turns around

Question 13

Which of the following is the correct application of the Leading Coefficient Test for $$f(x) = -x^4$ + 2x^2$ - 3$$?

Accepted Answer

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

Question 14

A polynomial function $$f(x)$$ has degree 7. What is the maximum number of turning points its graph can have?

Accepted Answer

6

Question 15

If $$f(x) = x^2$(x - 1)^3$, which statement is true about the x-intercepts?

Accepted Answer

The graph touches and turns around at $$x = 0$$ and crosses at $$x = 1 ($$with flattening)

Polynomial Functions and Their Graphs: Study Notes for College Algebra

Study Guide - Practice Questions

Study Guide - Flashcards