Polynomials & Transformations

Polynomial Graphs, Zeros, and Factors

100

Find the degree of the polynomial:

f(x) = -55x² + 14x³ - 2x⁴ + x - 19

4

200

What is the leading coefficient of the polynomial:

f(x) = -5x² +2x⁴ +1

2

300

Find the y-intercept of the polynomial:

f(x) = 52x + 14x³  - 25 - 15x²

-25

400

Find the zeros of the polynomial:

f(x)= -51x² + 378 + x⁴ - 9x + x³

-7, -3, 3, 6

500

Find the factors of the polynomial

f(x)= 3x³ +70 + x⁴ -35x² - 39x

(x + 7)(x + 2)(x - 1)(x - 5)

End Behavior

100

Given:  f(x) = (.5)^x​

What is the end behavior?

​​​

As x approaches negative infinity, y approaches infinity and

as x approaches positive infinity, y approaches 0

200

Given:  f(x) = 2^x + 1

What is the end behavior?

As x approaches negative infinity, y approaches 1 and 

as x approaches infinity, y approaches infinity.

300

Given:  f(x) = 3^x-5 +7

What is the end behavior?

As x approaches negative infinity, y approaches 7 and 

as x approaches infinity, y approaches infinity

400

Given f(x) = (.25)^x+2 + 8

What is the end behavior?

As x approaches negative infinity, y approaches infinity and

as x approaches infinity, y approaches 8

500

Given:  f(x) = (.33333)^x - 3

What is the end behavior?

As x approaches negative infinity, y approaches infinity and

as x approaches infinity, y approaches negative 3

Factoring

100

Factor:

x² - 25

(x + 5) (x - 5)

200

Factor:

16 - x²

(4 - x) (4 + x)

300

Factor:

49 - x⁴

(7 - x² ) (7 + x² )

400

Factor:

x⁴ - 81

(3 + x) (3 - x) (9 + x²)

500

Factor:

625 - x⁴

(5 +x) (5 - x) (25 +x²) 

Transformations

100

State the parent graph, the transformation from parent and asymptote for:     y = (3)^{x - 3} - 6

Parent:  y = (3)^x  

Transformation:  right 3, down 6

Asymptote:  y = -6

200

State the parent, transformation, and asymptote for:  y = (1/3)^x-1 

parent:  (.33333)^{x -1}

tranformation:  moves right 1

asymptote:  y = 0

300

State the parent, transformation and asymptote for

y = (5)^{x - 1} - 7

Parent y = (5)^x

transformation:  moves right 1 and down 7

asymptote:  y = -7

400

State the parent, transformation, and asymptote for:

y = (.25)^{x + 2} + 8

parent y = (.25)^x

transformation:  moves left 2 and up 8

asymptote:  y = 8

500

State the parent, transformation, and asymptote for

y = (9)^x

parent:  y = (9)^x

transformation:  none

asymptote:  y = 0

Average Rate of Change

100

Given:   f(x) = (.5)^x

State average rate of change for  -3 < x < -1

-3

200

Given:  f(x) = (3)^x - 4 find 

avg rate of change  0 < x < 2

4

300

Given: f(x) = (.5)^x - 2 find avg rate of change -3 < x < -1

-3

400

Given:  f(x) = (2)^{x + 5} - 7, find avg rate of change -4 < x < -1

14/3

500

Given: f(x) = (5)^{x + 1} -7, find avg rate of change 1 < x < 4

3100/3