Chapter 3: Polynomial Functions

Question 1

What is the form for a polynomial function?

Answer 1

f(x) = anx^n + an-1x^n-1 + … + a2x^2 + a1x^1 + a0x^0 (a)

a function where a is an integer and x is a variable with a positive whole number exponent

Question 2

What is NOT considered a polynomial function?

Answer 2

• anything that has a fractional exponent or a decimal exponent is NOT a polynomial function
• anything that has a negative exponent is NOT a polynomial function
• anything that involves decimals or fractions (in general) is NOT a polynomial function
• a radical function is NOT a polynomial function
• an absolute value function is NOT a polynomial function
• an exponential function is NOT a polynomial function
• vertical lines are NOT polynomial functions -> they’re not functions to begin with because they fail the VLT

Question 3

What criteria must a function met in order to be considered a polynomial function?

Answer 3

• variables that have whole number exponents
• should be written in decreasing order (not always given as this though)
• always have a constant (if you don’t see the constant, that means that its 0)
• always have a coefficient (if you don’t see a term, that means the coefficient for x is 0)

Question 4

What is the degree of a polynomial function? How do you find it?

Answer 4

The degree of a polynomial function is simply the LARGEST EXPONENT “n”

Question 5

What is the end behaviour?

Answer 5

The description of how the “y” values change as the “x” values increase.

AKA: As x increases, what is happening to y?

Usually follows the form:
“line extends…” or “curve extends…”

Question 6

What is the constant term?

Answer 6

a0 -> the number by itself

x^0 is not present because x^0 = 1

Question 7

What is the leading coefficient? (LC)

Answer 7

an -> the coefficient of the FIRST TERM with the LARGEST EXPONENT

Question 8

What are the x-intercepts?

Answer 8

Where the function crosses the x-axis

(x,0) or when y=0 what is x?

Question 9

What is the y-intercept?

Answer 9

Where the function crosses the y-axis

(0,y) or when x=0, what is y?

Question 10

What are the six polynomial functions?

Answer 10

1. Constant function
2. Linear function
3. Quadratic function
4. Cubic function
5. Quartic function
6. Quintic function

Question 11

What is the constant function? (degree, # of x-intercepts, characteristics)

Answer 11

Degree: 0
# of x-ints: 0 or infinite

Question 12

What is the linear function? (degree, # of x-intercepts, characteristics)

Answer 12

Degree: 1 ODD
# of x-ints: 1
NONE opposite directions
LC+ (up/down Q1/Q3) LC- (up/down Q2/Q4)

Question 13

What is the quadratic function? (degree, # of x-intercepts, characteristics)

Answer 13

Degree: 2 EVEN
# of x-ints: 0,1,2
MIN/MAX same direction
LC+ (up Q1/Q2) LC- (down Q3/Q4)

Question 14

What is the cubic function? (degree, # of x-intercepts, characteristics)

Answer 14

Degree: 3 ODD
# of x-ints: 1,2,3
NONE opposite directions
LC+ (up/down Q1/Q3) LC- (up/down Q2/Q4)

Question 15

What is the quartic function? (degree, # of x-intercepts, characteristics)

Answer 15

Degree: 4 EVEN
# of x-ints: 0,1,2,3,4
MIN/MAX same direction
LC+ (up Q1/Q2) LC- (down Q3/Q4)

Question 16

What is the quintic function? (degree, # of x-intercepts, characteristics)

Answer 16

Degree: 5 ODD
# of x-ints: 1,2,3,4,5
NONE opposite directions
LC+ (up/down Q1/Q3) LC- (up/down Q2/Q4)