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Parent Equation

Parent Equation. General Forms Transforming. Parent Equation. The simplest form of any function Each parent function has a distinctive graph We will summarize these in the next few slides. Constant. f(x)=a; where a is any number. Linear. f(x)=x. Absolute Value. Exponential Value.

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Parent Equation

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  1. Parent Equation General Forms Transforming

  2. Parent Equation • The simplest form of any function • Each parent function has a distinctive graph • We will summarize these in the next few slides

  3. Constant • f(x)=a; where a is any number

  4. Linear • f(x)=x

  5. Absolute Value

  6. Exponential Value

  7. Logarithmic • y=lnx

  8. Square Root/Radical

  9. Cube Root

  10. Quadratic • f(x)=x2

  11. Cubic • f(x)=x3

  12. Reciprocal • Same as a Rational Graph

  13. Rational

  14. Sine • y=sinx

  15. Cosine • y=cosx

  16. Tangent • y=tanx

  17. Constant Function • f(x)=a; where a is any number • Domain: all real numbers • Range: a

  18. Linear Function • f(x)=x • Domain: all real numbers • Range: all real numbers

  19. Transformations Linear and Quadratic

  20. Vertical Translations • Positive Shift (Shift up) • Form: y=f(x)+b where b is the shift up • Negative Shift (Shift down) • Form: y=f(x)-b where b is the shift down

  21. Horizontal Translations • Shift to the right • Form: y=f(x-h) • The negative makes you think left, but actually means right here • Shift to the left • Form y=f(x+h) • This would shift to the left of the origin

  22. Vertical Stretch and Compression • If y=f(x), then y=af(x) gives a vertical stretch or compression of the graph of f • If a>1, the graph is stretched vertically by a factor of a • If a<1, the graph is compressed vertically by a factor of a

  23. Horizontal Stretch and Compression • If y=f(x),then y=f(bx) gives a horizontal stretch or compression of the graph of f • If b>1, the graph is compressed horizontally by a factor of 1/b • If b<1, the graph is stretched horizontally by a factor of 1/b

  24. Reflection • If y=f(x), then y=-f(x) gives a reflection of the graph f across the x axis • If y=f(x), then y= f(-x) gives a reflection of the graph f across the y axisl

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