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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
9. Section 3.5
Graph the following functions:
9. y = 3(x2)2 + 1 10. y = 10. 1
3 11. 11. h(x) = 4
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 ...
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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.
- Fall '08