PARENT FUNCTIONS Pre-Ap Algebra 2 Complete your Parent Function Packet!!!! There are two slides per Parent Function. The Parent Functions are numbered in the bottom right corner of each slide. The Function name and equation are at the top of each slide. Your packet does not have a heading for zeros so be sure to add it to the information as you complete each Parent function. You do not have to write down the tables we will talk about and add them as we go. You will not have time in class to complete this packet. (A total of 4 cards! This packet will be part of your notes Quiz at the end of each si weeks.
Constant Function f ( ) c; c 4 Calculator: y 4 Domain: ε or ε (-, ) Range: y 4 Zeros: None X-Intercept: none Y-Intercept: (0,4) Even function Constant Function f ( ) c; c 4 Symmetry: y-ais Even Function Ma: None Increasing: No Decreasing: No 2
Linear Function f ( ) Calculator: y Domain: ε or ε (-, ) Range: y ε or y ε (-, ) Zeros: (0,0) or 0 X-Intercept: (0,0) Y-Intercept: (0,0) 2 Linear Function f ( ) Symmetry: Origin Odd Function Ma: None Increasing: ε (-, ) Decreasing: Never 2 3
Absolute Value Function f ( ) Calculator: y abs () y Domain: ε or ε (-, ) Range: y 0 or y ε [0, ) Zeros: (0,0) or 0 X-Intercept: (0,0) Y-Intercept: (0,0) 3 Absolute Value Function f ( ) Symmetry: y-ais Even Function Ma: none Min: (0,0) Increasing: ε (0, ) Decreasing: ε (-,0) 3 4
Quadratic Function 2 f ( ) Calculator: y ^2 Domain: ε or ε (-, ) Range: y 0 or y ε [0, ) Zeros: (0,0) or 0 X-Intercept: 0 or (0,0) Y-Intercept: y 0 or (0,0) 4 Quadratic Function 2 f ( ) Symmetry: y-ais Even Function Ma: None Min: (0,0) Increasing: (0, ) Decreasing: (-,0) 4 5
Square Root Function (Radical Function) f ( ) Calculator: y ( ) Domain: 0 or ε [0, ) Range: y 0 or y ε [0, ) Zeros: (0,0) or 0 X-Intercept: (0,0) Y-Intercept: (0,0) 5 Square Root Function (Radical Function) f ( ) Symmetry: None Neither Odd or Even Ma: None Min: (0,0) Increasing: ε (0, ) Decreasing: None 5 6
Cubic Function f ( ) 3 Calculator: y ^3 Domain: ε or ε (-, ) Range: y ε or y ε (-, ) Zeros: (0,0) or 0 X-Intercept: (0,0) Y-Intercept: (0,0) 6 Cubic Function 3 f ( ) Symmetry: Origin Odd Function Ma: None Increasing: ε (-, ) Decreasing: None 6 7
Cube Root Function (Radical Function) f ( ) 3 Calculator: y Domain: ε or ε (-, ) Range: y ε or ε (-, ) Zeros: (0,0) or 0 X-Intercept: (0,0) Y-Intercept: (0,0) 3 7 Cube Root Function (Radical Function) f ( ) 3 Symmetry: Origin Odd Function Ma: None Increasing: ε (-, ) Decreasing: Never 7 8
Rational Odd Function (Reciprocal Function) f ( ) Calculator: y / Domain: ε, 0 or ε (-,0) U (0, ) Range: y ε, y 0 or y ε (-,0) U (0, ) Zeros: none X-Intercept: none Y-Intercept: none 8 Rational Odd Function (Reciprocal Function) f ( ) Symmetry: Origin Odd Function Ma: None Increasing: Never Decreasing: ε (-,0) U (0, ) Vertical Asymptotes: 0 Horizontal Asymptotes: y 0 8 9
Rational Even Function (Reciprocal Function) f ( ) 2 Calculator: y / (^2) Domain: ε (-,0) U (0, ) Range: y > 0 or y ε (0, ) Zeros: none X-Intercept: none Y-Intercept: none 9 Rational Function (Even) f ( ) 2 Symmetry: y-ais Even Function Ma: None Increasing: ε (-,0) Decreasing: ε (0, ) Vertical Asymptotes: 0 Horizontal Asymptotes: y 0 9 0
Eponential Function (Decreasing) f ( ) b 0 < b < ; b 2 Calculator: y ½^ y ½ Domain: ε or ε (-, ) Range: y > 0 or y ε (0, ) Zeros: none X-Intercept: none Y-Intercept: (0,) 0 Eponential Function (Decreasing) f ( ) b 0 < b < ; b 2 Symmetry: None Neither Even or odd Ma: None Increasing: Never Decreasing: ε (-, ) Horizontal Asymptotes: Y 0 0
Eponential Function (Increasing) f ( ) b b > ; b 2 Calculator: y 2^ Domain: ε or ε (-, ) Range: y > 0 or y ε (0, ) Zeros: none X-Intercept: none Y-Intercept: (0,) Eponential Function (Increasing) f ( ) b b > ; b 2 Symmetry: None Neither Even or Odd Ma: None Increasing: ε (-, ) Decreasing: None Horizontal Asymptotes: Y 0 2
Eponential Base e Function f ( ) e Calculator: y e Domain: ε (-, ) Range: y > 0 or y ε (0, ) Zeros: none X-Intercept: none Y-Intercept: (0,) 2 Eponential Base e Function f ( ) e Symmetry: None Neither Even or Odd Ma: None Increasing: ε (-, ) Decreasing: Never Horizontal Asymptotes: Y 0 2 3
Logarithmic Function (Common) f ( ) log 0 b > ; b 0 Calculator: y log() Domain: > 0 or ε (0, ) Range: y ε or y ε (-, ) Zeros: (,0) or X-Intercept: (,0) Y-Intercept: none 3 Logarithmic Function (Common) f ( ) log 0 b > ; b 0 Symmetry: None Neither Even or Odd Ma: None Increasing: ε (0, ) Decreasing: Never Vertical Asymptotes: 0 3 4
Logarithmic Function (Natural) f ( ) ln e Calculator: y ln() Domain: > 0 or ε (0, ) Range: y ε or y ε (-, ) Zeros: (,0) or X-Intercept: (,0) Y-Intercept: none 4 Logarithmic Function (Natural) f ( ) ln e Symmetry: None Neither Even or Odd Ma: None Increasing: ε (0, ) Decreasing: Never Vertical Asymptotes: 0 4 5