3-5 Transformations - 3-5 Transformations Vertical Shifts...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3-5: Transformations Vertical Shifts: If a real number c is added to the function y = f(x), the graph of the new function y = f(x) + c is the graph of f shifted up if c > 1, down if c < 1. Horizontal Shifts: If x in a function y = f(x) is replaced by x – c (c a real number), the graph of the new function y = f(x ­ c) is shifted horizontally left if c < 0) or right if c > 0. Stretches and compressions: When a function y = f(x) is multiplied by a positive number k, the graph of the new function y = kf(x) is vertically compressed if 0 < k < 1 or stretched if k > 1. Reflection about the x­axis: When the function y = f(x) is multiplied by –1, the graph of the new function y = ­f(x) is the reflection about the axis. Graph: (1) a. y = f(x) = | x| b. y = f(x) = | x| - 3 (3) a. y = f(x) = b. y = f(x) = - x x c. y = f(x) = | x - 2| d. y = f(x) = | x - 2| - 3 c. y = f(x) = d. y = f(x) = -3 −x x +3 +4 (2) a. y = f(x) = x2 b. y = f(x) = 2x2 c. y = f(x) = ½x2 TRY THESE SECTION 3.4: Classify each of the following functions or graphs as Constant, Linear, Identity, Square, Cube, Square Root, or Absolute Value: 1. f(x) = 5x 2. f(x) = x 3. f(x) = ­4 4. 5. 6. 7. For the following function, (a) find the domain, (b) graph it, (c) locate any intercepts, (d) find the range: 2x + 5 ­ 7 ≤ x < ­1 ­1≤x<0 8. f ( x ) = ­2 x2 x≥0 8. 9. Section 3.5 Graph the following functions: 9. y = 3(x­2)2 + 1 10. y = ­ 10. 1 x+2 ­1 3 11. 11. h(x) = 4 +2 x If y1 = x3 + x2, then identify each of the following as reflections across the x­axis, y­axis, origin, or none of the preceding: 12. y2 = ­x3 + x2 13. y3 = ­x3 ­ x2 14. y4 = x3 ­ x2 ...
View Full Document

This note was uploaded on 01/04/2012 for the course MAC 1105 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.

Page1 / 2

3-5 Transformations - 3-5 Transformations Vertical Shifts...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online