Function Parent Graph Characteristics Name Function

1 Copyright 2011 2016 by Harold Toomey, WyzAnt Tutor 1 Harold s Parent functions Cheat Sheet 20 September 2016 Function Name Parent Function Graph Characteristics Algebra Constant Domain: ( , ) Range: [c, c] Inverse Function : Undefined (asymptote) Restrictions: c is a real number Odd/Even: Even General Form: 0 Linear or Identity Domain: ( , ) Range: ( , ) Inverse Function : Restrictions: m 0 Odd/Even: Odd General Forms: 0 Quadratic or Square Domain: ( , ) Range: [0, ) Inverse Function : Restrictions: None Odd/Even: Even General Form: 0 Square Root Domain: [0, ) Range: [0, ) Inverse Function : x Restrictions: 0 Odd/Even: Neither General Form: Function Name Parent Function Graph Characteristics Copyright 2011 2016 by Harold A.]]]

2 Toomey, WyzAnt Tutor 2 Absolute Value | | Domain: ( , ) Range: [0, ) Inverse Function : 0 Restrictions: 0 , 0 , Odd/Even: Even General Form: | | Cubic Domain: ( , ) Range: ( , ) Inverse Function : Restrictions: None Odd/Even: Odd General Form: Cube Root Domain: ( , ) Range: ( , ) Inverse Function : Restrictions: None Odd/Even: Odd General Form: Exponential 10 Domain: ( , ) Range: (0, ) Inverse Function : log ln Restrictions: None, x can be imaginary Odd/Even: Neither General Form: 10 Logarithmic log ln Domain: (0, ) Range: ( , ) Inverse Function : 10 Restrictions: x > 0 Odd/Even: Neither General Form: log Function Name Parent Function Graph Characteristics Copyright 2011 2016 by Harold A.]

3 Toomey, WyzAnt Tutor 3 Reciprocal or Rational 1 Domain: ( , 0) (0, ) Range: ( , 0) (0, ) Inverse Function : 1 Restrictions: x 0 Odd/Even: Odd General Form: Greatest Integer or Floor Domain: ( , ) Range: ( , ) whole numbers only Inverse Function : Undefined (asymptotic) Restrictions: Real numbers only Odd/Even: Neither General Form: Inverse functions , Domain of x Domain of y Range of y Range of x Inverse Function : By definition Restrictions: None Odd/Even: Odd General Form: Conic Sections Circle Domain: , Range: , Inverse Function : Same as Parent Restrictions: None Odd/Even: Both Focus : , General Forms: 0 0 Function Name Parent Function Graph Characteristics Copyright 2011 2016 by Harold A.

4 Toomey, WyzAnt Tutor 4 Ellipse 1 Domain: , Range: , Inverse Function : 1 Restrictions: None Odd/Even: Both Foci : General Forms: 1 0 where 4 0 Parabola Domain: ( , ) Range: , or , Inverse Function : Restrictions: None Odd/Even: Even Vertex : , Focus : , General Forms: 4 0 where 4 0 Hyperbola 1 Domain: ( , a+h] [a+h, ) Range: ( , ) Inverse Function : 1 Restrictions: Domain is restricted Odd/Even: Both Foci : General Forms: 1 0 where 4 0 Function Name Parent Function Graph Characteristics Copyright 2011 2016 by Harold A.

5 Toomey, WyzAnt Tutor 5 Trigonometry Sine Domain: ( , ) Range: [ 1, 1] Inverse Function : Restrictions: None Odd/Even: Odd General Form: Cosine Domain: ( , ) Range: [ 1, 1] Inverse Function : Restrictions: None Odd/Even: Even General Form: Tangent Domain: ( , ) except for Range: ( , ) Inverse Function : Restrictions: Asymptotes at Odd/Even: Odd General Form: Secant sec 1 Domain: ( , ) except for Range: ( , 1] [1, ) Inverse Function : Restrictions: Range is bounded Odd/Even: Even General Form: Cosecant 1 Domain: ( , ) except for Range: ( , 1] [1, ) Inverse Function : Restrictions: Range is bounded Odd/Even: Odd General Form: Cotangent 1 Domain: ( , ) except for Range: ( , ) Inverse Function : Restrictions: Asymptotes at x = Odd/Even: Odd General Form: Function Name Parent Function Graph Characteristics Copyright 2011 2016 by Harold A.

6 Toomey, WyzAnt Tutor 6 Arcsine Domain: [ 1, 1] Range: , or Quadrants I & IV Inverse Function : Restrictions: Range & Domain are bounded Odd/Even: Odd General Form: Arccosine Domain: [ 1, 1] Range: 0, or Quadrants I & II Inverse Function : Restrictions: Range & Domain are bounded Odd/Even: None General Form: Arctangent Domain: ( , ) Range: , or Quadrants I & IV Inverse Function : Restrictions: Range is bounded Odd/Even: Odd General Form: Arcsecant Domain: ( , 1] [1, ) Range: 0, ( , or Quadrants I & II Inverse Function : Restrictions: Range & Domain are bounded Odd/Even: Neither General Form: Arccosecant Domain: ( , 1] [1, ) Range: ,0 0, or Quadrants I & IVInverse Function : Restrictions: Range & Domain are bounded Odd/Even: Odd General Form: Arccotangent Domain: ( , ) Range: 0, or Quadrants I & II Inverse Function : Restrictions: Range is bounded Odd/Even: Neither General Form.)

7 Function Name Parent Function Graph Characteristics Copyright 2011 2016 by Harold A. Toomey, WyzAnt Tutor 7 Hyperbolics Hyperbolic Sine sinh 2 Domain: ( , ) Range: ( , ) Inverse Function : Restrictions: None Odd/Even: Odd General Form: Hyperbolic Cosine 2 Domain: ( , ) Range: [1, ) Inverse Function : Restrictions: None Odd/Even: Even General Form: Hyperbolic Tangent 1 1 Domain: ( , ) Range: ( 1, 1) Inverse Function : Restrictions: Asymptotes at 1 Odd/Even: Odd General Form.]

8 Hyperbolic Secant sech 1 Domain: ( , ) Range: (0, 1] Inverse Function : Restrictions: Asymptote at 0 Odd/Even: Even General Form: Hyperbolic Cosecant 1 Domain: ( , 0) (0, ) Range: ( , 0] [0, ) Inverse Function : Restrictions: Asymptotes at 0, 0 Odd/Even: Odd General Form: Hyperbolic Cotangent 1 1 Domain: ( , 0) (0, ) Range: ( , 1) (1, ) Inverse Function : Restrictions: Asymptotes at 0, 1 Odd/Even: Odd General Form: Function Name Parent Function Graph Characteristics Copyright 2011 2016 by Harold A.)

9 Toomey, WyzAnt Tutor 8 Hyperbolic Arcsine 1 Domain: ( , ) Range: ( , ) Inverse Function : Restrictions: None Odd/Even: Odd General Form: Hyperbolic Arccosine 1 Domain: [1, ) Range: [0, ) Inverse Function : Restrictions: 0 Odd/Even: Neither General Form: Hyperbolic Arctangent 12 1 1 Domain: ( 1, 1) Range: ( , ) Inverse Function : Restrictions: Asymptotes at 1 Odd/Even: Odd General Form: Hyperbolic Arcsecant 1 1 1 Domain: (0, 1] Range: [0, ) Inverse Function : Restrictions: Odd/Even: Neither General Form: Hyperbolic Arccosecant 1 1 1 Domain: ( , 0) (0, ) Range: ( , 0] [0, ) Inverse Function : Restrictions: Asymptotes at 0, 0 Odd/Even: Odd General Form: Hyperbolic Arccotangent 12 1 1 Domain: , 1 1, Range: ,0 0, Inverse Function : Restrictions: Asymptotes at 0, 1 Odd/Even: Odd General Form.]]

10 Copyright 2011 2016 by Harold Toomey, WyzAnt Tutor 9 Graphing Tips All functions The Seven Function Levers y = a f (b (x h)) + k Graphing Tips 1) Move up/down k (Vertical translation) + Moves it up 2) Move left/right h (Horizontal translation) + Moves it right 3) Stretch up/down a (Vertical dilation) Larger stretches it taller or makes it grow faster 4) Stretch left/right b (Horizontal dilation) Larger stretches it wider 5) Flip about x axis a a If then odd Function 6) Flip about y axis b b If then even Function 7) Rotate CW/CCW cot2 A CB + rotates CCW For conic sections, where: 0 Trigonometric functions The Six Trig Levers y = a sin (b (x h)) + k Graphing Tips Notes 1) Move up/down k (Vertical translation) k max min 2 If then x