pdf fraction cheat sheet, Cheat Sheet of Mathematics

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2023/2024

Uploaded on 09/20/2023

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Practice: Key Features of Graphs Name ________________________________
Directions: Given the graphs below, find the key features (domain, range, intercepts,
increasing/decreasing intervals, maximum/minimum, positive/negative) of each graph.
Graph
Key Features of Graph
1.
Domain: [-3,14] Increasing: (-3,9)๊“ด(11,14)
Range: [-5,10] Decreasing: (9,14)
x-intercept(s): (4.5,0) Positive: (4.5,14]
y-intercept: (0,-3) Negative: [-3,4.5)
Maximum: (9,10) Minimum: Rel: (-3,-5)
End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’3, ๐‘ฆ โ†’ โˆ’5; ๐‘Ž๐‘  ๐‘ฅ โ†’ 14, ๐‘ฆ โ†’ 10
2.
Domain: (-โˆž, โˆž) Increasing: (-2,-0.5) ๊“ด (1, โˆž)
Range: (0, โˆž) Decreasing: (-โˆž,-2) ๊“ด (-0.5,1)
x-intercept(s): (-2,0) & (1,0) Positive: (-โˆž,-2) ๊“ด (-2,1) ๊“ด(1, โˆž)
y-intercept: (0,4) Negative: none
Maximum: Rel: (-0.5,5.063) Minimum: (-2,0) & (1,0)
End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’โˆž, ๐‘ฆ โ†’ +โˆž; ๐‘Ž๐‘  ๐‘ฅ โ†’ +โˆž, ๐‘ฆ โ†’ +โˆž
3.
Domain: (-โˆž, โˆž) Increasing: (-2,1.333)
Range: (-โˆž, โˆž) Decreasing: (-โˆž,-2) ๊“ด (1.333, โˆž)
x-intercept(s): (-2,0) & (3,0) Positive: (-โˆž,-2) ๊“ด (-2,3)
y-intercept: (0,3) Negative: (3, โˆž)
Maximum: L(1.333,4.63) Minimum: L(-2,0)
End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’โˆž, ๐‘ฆ โ†’ +โˆž; ๐‘Ž๐‘  ๐‘ฅ โ†’ +โˆž, ๐‘ฆ โ†’ โˆ’โˆž
4.
Domain: (-โˆž, โˆž) Increasing: (2, โˆž)
Range: (1, โˆž) Decreasing: (-โˆž,2)
x-intercept(s): none Positive: (-โˆž, โˆž)
y-intercept: (0,5) Negative: none
Maximum: none (unbounded) Minimum: (2,1)
End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’โˆž, ๐‘ฆ โ†’ +โˆž; ๐‘Ž๐‘  ๐‘ฅ โ†’ +โˆž, ๐‘ฆ โ†’ +โˆž
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Practice: Key Features of Graphs Name ________________________________

Directions: Given the graphs below, find the key features (domain, range, intercepts, increasing/decreasing intervals, maximum/minimum, positive/negative) of each graph.

Graph Key Features of Graph

  1. Domain: [-3,14] Increasing: (-3,9)๊“ด(11,14) Range: [-5,10] Decreasing: (9,14) x-intercept(s): (4.5,0) Positive: (4.5,14] y-intercept: (0,-3) Negative: [-3,4.5) Maximum: (9,10) Minimum: Rel: (-3,-5) End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’ 3 , ๐‘ฆ โ†’ โˆ’ 5 ; ๐‘Ž๐‘  ๐‘ฅ โ†’ 14 , ๐‘ฆ โ†’ 10
  2. Domain: (-โˆž, โˆž) Increasing: (-2,-0.5) ๊“ด (1, โˆž) Range: (0, โˆž) Decreasing: (-โˆž,-2) ๊“ด (-0.5,1) x-intercept(s): (-2,0) & (1,0) Positive: (-โˆž,- 2 ) ๊“ด (-2,1) ๊“ด(1, โˆž) y-intercept: (0,4) Negative: none Maximum: Rel: (-0.5,5.063) Minimum: (-2,0) & (1,0) End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’โˆž, ๐‘ฆ โ†’ +โˆž; ๐‘Ž๐‘  ๐‘ฅ โ†’ +โˆž, ๐‘ฆ โ†’ +โˆž
  3. Domain: (-โˆž, โˆž) Increasing: (-2,1.333) Range: (-โˆž, โˆž) Decreasing: (-โˆž,-2) ๊“ด (1.333, โˆž) x-intercept(s): (-2,0) & (3,0) Positive: (-โˆž,-2) ๊“ด (-2,3) y-intercept: (0,3) Negative: (3, โˆž) Maximum: L(1.333,4.63) Minimum: L(-2,0) End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’โˆž, ๐‘ฆ โ†’ +โˆž; ๐‘Ž๐‘  ๐‘ฅ โ†’ +โˆž, ๐‘ฆ โ†’ โˆ’โˆž
  4. Domain: (-โˆž, โˆž) Increasing: ( 2 , โˆž) Range: (1, โˆž) Decreasing: (-โˆž, 2 ) x-intercept(s): none Positive: (-โˆž, โˆž) y-intercept: (0,5) Negative: none Maximum: none (unbounded) Minimum: (2,1) End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’โˆž, ๐‘ฆ โ†’ +โˆž; ๐‘Ž๐‘  ๐‘ฅ โ†’ +โˆž, ๐‘ฆ โ†’ +โˆž

Practice: Key Features of Graphs Name ________________________________

  1. Domain: (-โˆž, โˆž) Increasing: none Range: (-โˆž, โˆž) Decreasing: (-โˆž, โˆž) x-intercept(s): (8,0) Positive: (-โˆž,8) y-intercept: (0,4) Negative: (8, โˆž) Maximum: none (unbounded) Minimum: none (unbounded) End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’โˆž, ๐‘ฆ โ†’ +โˆž; ๐‘Ž๐‘  ๐‘ฅ โ†’ +โˆž, ๐‘ฆ โ†’ โˆ’โˆž
  2. Domain: (-โˆž, โˆž) Increasing: (-โˆž, โˆž) Range: (0, โˆž) Decreasing: none x-intercept(s): none Positive: (-โˆž, โˆž) y-intercept: (0,1) Negative: none Maximum: none (unbounded) Minimum: none (unbounded) End Behavior: ๐‘Ž๐‘  ๐‘ฅ โ†’ โˆ’โˆž, ๐‘ฆ โ†’ 0 ; ๐‘Ž๐‘  ๐‘ฅ โ†’ +โˆž, ๐‘ฆ โ†’ +โˆž