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

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

Study Guide - Practice Questions