1. Algebra 2/Trigonometry Name __________________________
End Behavior Worksheet Date ________________ Block _____
A. Given each function, identify the degree, leading coefficient, and describe the end behavior using proper notation. You are NOT ALLOWED TO USE A GRAPHING CALCULATOR!
Function
Degree
Leading Coefficient
End Behavior
1) 𝑓 𝑥 = 𝑥 3 −2 𝑥 2 −𝑥+1
As x →- ∞, f(x) → _______
As x → ∞, f(x) →________
2) 𝑓 𝑥 = 2𝑥 5 +2 𝑥 2 −5𝑥+1
3) 𝑓 𝑥 =− 2𝑥 5 − 𝑥 2 +5𝑥+3
4) 𝑓 𝑥 = −𝑥 3 +5𝑥−2
5) 𝑓 𝑥 =2 𝑥 2 +3𝑥−4
6) 𝑓 𝑥 = 𝑥 4 −3 𝑥 2 +2𝑥+1
B. Match each of the graphs with the equations provided below. You are NOT ALLOWED TO USE A GRAPHING CALCULATOR!
____ 1) 𝑓 𝑥 =−2𝑥 ____ 2) 𝑓 𝑥 = 𝑥 2 −4𝑥 ____ 3) 𝑓 𝑥 =−2 𝑥 2 −5𝑥
____ 4) 𝑓 𝑥 =2 𝑥 3 −3𝑥+1 _______ 5) 𝑓 𝑥 = 𝑥 4 +2 𝑥 ____ 6) 𝑓 𝑥 =− 1 4 𝑥 4 +3 𝑥 2
____ 7) 𝑓 𝑥 =− 1 3 𝑥 3 + 𝑥 2 − ____ 8) 𝑓 𝑥 = 1 5 𝑥 5 −2 𝑥 𝑥

2. C. Review – Find all zeros (real and imaginary) by factoring and/or taking the square root. Leave your answers in simplified radical/fractional form.
1) 𝑥 2 −25=0
2) 𝑥 2 −6𝑥+9=0
Zeros: ____________________________ Zeros: ___________________________
3) 𝑥 3 −4 𝑥 2 +4𝑥=0
4) 𝑥 4 − 𝑥 2 −20=0
Zeros: ____________________________ Zeros: ___________________________
5) 𝑥 3 +3 𝑥 2 −4𝑥−12=0
6) 𝑥 3 − 4𝑥 2 −25𝑥+100=0
Zeros: ____________________________ Zeros: ___________________________
7) 5𝑥 3 −5 𝑥 2 =10𝑥
8) 𝑥 4 +3 𝑥 2 =−2
Zeros: ____________________________ Zeros: ___________________________