Question

nc math 3
practice - key features of functions: end behavior
name: sydney
date: 1-16 block: 2

1. positive or negative?

even or odd?
state the end behavior.

1. ( f(x) = -x^4 + 6x^3 - x + 9 )

positive or negative?
even or odd?
state the end behavior.

1. positive or negative?

even or odd?
state the end behavior.

1. ( y = -4x^3 + 2x + 7 )

positive or negative?
even or odd?
state the end behavior.

1. positive or negative?

even or odd?
state the end behavior.

1. ( h(x) = 2x^5 + 6x^4 - x )

positive or negative?
even or odd?
state the end behavior.

1. match the graph with the end behavior.

a.
____ as ( x ) approaches ( infty ), ( y ) approaches ( -infty ) and as ( x ) approaches ( -infty ), ( y ) approaches ( -infty )
b.
____ as ( x ) approaches ( infty ), ( y ) approaches ( -infty ) and as ( x ) approaches ( -infty ), ( y ) approaches ( infty )
c.
____ as ( x ) approaches ( infty ), ( y ) approaches ( infty ) and as ( x ) approaches ( -infty ), ( y ) approaches ( -infty )
d.
____ as ( x ) approaches ( infty ), ( y ) approaches ( infty ) and as ( x ) approaches ( -infty ), ( y ) approaches ( infty )

Explanation:

---

Problem 1

Step1: Identify leading term sign

Leading term: Implied positive (even-degree V-shape), so Positive

Step2: Check symmetry (even/odd)

Graph symmetric over y-axis, so Even

Step3: State end behavior

As $x \to \infty$, $y \to \infty$; As $x \to -\infty$, $y \to \infty$
---

Problem 2

Step1: Identify leading term sign

Leading term: $-x^4$, sign is Negative

Step2: Check degree parity

Degree = 4 (even), so Neither (not symmetric over y-axis/origin)

Step3: State end behavior

As $x \to \infty$, $y \to -\infty$; As $x \to -\infty$, $y \to -\infty$
---

Problem 3

Step1: Identify leading term sign

Graph opens upward, leading term Positive

Step2: Check symmetry (even/odd)

Graph symmetric over y-axis, so Even

Step3: State end behavior

As $x \to \infty$, $y \to \infty$; As $x \to -\infty$, $y \to \infty$
---

Problem 4

Step1: Identify leading term sign

Leading term: $-4x^3$, sign is Negative

Step2: Check degree parity

Degree = 3 (odd), so Neither (not symmetric over origin)

Step3: State end behavior

As $x \to \infty$, $y \to -\infty$; As $x \to -\infty$, $y \to \infty$
---

Problem 5

Step1: Identify end behavior from graph

As $x \to \infty$, $y \to -\infty$; As $x \to -\infty$, $y \to -\infty$

Step2: Deduce leading term sign/degree

Even degree, negative leading term: Negative

Step3: Check symmetry (even/odd)

Graph symmetric over y-axis, so Even
---

Problem 6

Step1: Identify leading term sign

Leading term: $2x^5$, sign is Positive

Step2: Check degree parity

Degree = 5 (odd), so Neither (not symmetric over origin)

Step3: State end behavior

As $x \to \infty$, $y \to \infty$; As $x \to -\infty$, $y \to -\infty$
---

Problem 7

Step1: Match Graph A to end behavior

Even degree, positive leading term: matches As $x \to \infty$, $y \to \infty$ and as $x \to -\infty$, $y \to \infty$

Step2: Match Graph B to end behavior

Odd degree, negative leading term: matches As $x \to \infty$, $y \to -\infty$ and as $x \to -\infty$, $y \to \infty$

Step3: Match Graph C to end behavior

Odd degree, positive leading term: matches As $x \to \infty$, $y \to \infty$ and as $x \to -\infty$, $y \to -\infty$

Step4: Match Graph D to end behavior

Even degree, negative leading term: matches As $x \to \infty$, $y \to -\infty$ and as $x \to -\infty$, $y \to -\infty$

Answer:

1. Positive or Negative? $\boldsymbol{\text{Positive}}$

Even or Odd? $\boldsymbol{\text{Even}}$
State the end behavior: $\boldsymbol{\text{As } x \to \infty, y \to \infty; \text{ As } x \to -\infty, y \to \infty}$

1. Positive or Negative? $\boldsymbol{\text{Negative}}$

Even or Odd? $\boldsymbol{\text{Neither}}$
State the end behavior: $\boldsymbol{\text{As } x \to \infty, y \to -\infty; \text{ As } x \to -\infty, y \to -\infty}$

1. Positive or Negative? $\boldsymbol{\text{Positive}}$

Even or Odd? $\boldsymbol{\text{Even}}$
State the end behavior: $\boldsymbol{\text{As } x \to \infty, y \to \infty; \text{ As } x \to -\infty, y \to \infty}$

1. Positive or Negative? $\boldsymbol{\text{Negative}}$

Even or Odd? $\boldsymbol{\text{Neither}}$
State the end behavior: $\boldsymbol{\text{As } x \to \infty, y \to -\infty; \text{ As } x \to -\infty, y \to \infty}$

1. Positive or Negative? $\boldsymbol{\text{Negative}}$

Even or Odd? $\boldsymbol{\text{Even}}$
State the end behavior: $\boldsymbol{\text{As } x \to \infty, y \to -\infty; \text{ As } x \to -\infty, y \to -\infty}$

1. Positive or Negative? $\boldsymbol{\text{Positive}}$

Even or Odd? $\boldsymbol{\text{Neither}}$
State the end behavior: $\boldsymbol{\text{As } x \to \infty, y \to \infty; \text{ As } x \to -\infty, y \to -\infty}$

1. $\boldsymbol{\text{D. } \text{As } x \to \infty, y \to -\infty \text{ and as } x \to -\infty, y \to -\infty}$

$\boldsymbol{\text{B. } \text{As } x \to \infty, y \to -\infty \text{ and as } x \to -\infty, y \to \infty}$
$\boldsymbol{\text{C. } \text{As } x \to \infty, y \to \infty \text{ and as } x \to -\infty, y \to -\infty}$
$\boldsymbol{\text{A. } \text{As } x \to \infty, y \to \infty \text{ and as } x \to -\infty, y \to \infty}$