Polynomial & Rational / Exponential & Logarithmic Functions

Leading Coefficient Test

100

x³+x²+4x-5

Leading coefficient: 1

Degree: 3

End behavior: Left down, right up

200

-2x⁶-3x⁴+4

Leading coefficient: -2

Degree: 6

End Behavior: Left down, right down

300

-3x⁵-7x⁴+x³+2x²+x-10

Leading coefficient: -3

Degree: 5

End behavior: Left up, right down

400

x²+3x-2+6x⁴

Leading coefficient: 6

Degree: 4

End behavior: Left up, right up

500

3x²-5x⁴+2x⁶+x³+x+4x⁵-6x⁷

Leading Coefficient: -6

Degree: 7

End Behavior: Left up, right down

Graphs of Polynomials

100

2x²-3x+1

Leading coefficient: positive

Degree: even

200

3x³-9x+1

Leading coefficient: positive

Degree: odd

300

-4x⁵+4

Leading coefficient: negative

Degree: odd

400

-2x⁴+4

Leading coefficient: negative

Degree: even

500

-3x⁵+2x

Leading coefficient: negative

Degree: odd

Exponential/Logarithmic

100

Which function has a horizontal asymptote of y=0 and a y-intercept at (0,1)?

Exponential function

200

State the asymptote and x-intercept for a parent logarithmic function. 

Asymptote: x=0 (vertical)

X-intercept: (1,0)

300

What is the range for the following equation?

y=2^x-5

Range: (-5, ∞)

400

What is the domain for the following equation?

y=log₇(x-3)

Domain: (3, ∞)

500

What is the domain and range for the following graph?

Domain: (-∞, ∞)

Range: (1, ∞)