sobirov javokhir on Ministry of Higher and Secondary Education of the Republic of Uzbekistan Tashkent region Chirchik State Pedagogical Institute, Faculty of Tourism, student of Tourism



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Functions

The Vertical Line Test

  • If it is possible for a vertical line to intersect a graph at more than one point, then the graph is NOT the graph of a function.
  • Page 117
  • (-3,3)
  • (4,4)
  • (1,1)
  • (1,-2)
  • Function?
  • No, Two points are on
  • The same vertical line.
  • Use the vertical line test to visually check if the relation is a function.
  • (-3,3)
  • (4,-2)
  • (1,1)
  • (3,1)
  • Use the vertical line test to visually check if the relation is a function.
  • Function?
  • Yes, no two points are
  • on the same vertical line

Examples

  • I’m going to show you a series of graphs. **don’t write 
  • Determine whether or not these graphs are functions.
  • You do not need to draw the graphs in your notes. **or write this note
  • #1
  • Function?
  • YES!
  • Function?
  • #2
  • YES!
  • Function?
  • #3
  • NO!
  • Function?
  • #4
  • YES!

Function?

  • #5
  • NO!
  • #6
  • Function?
  • YES!
  • Function?
  • #7
  • NO!
  • Function?
  • #8
  • NO!
  • #9
  • Function?
  • YES!

Function Notation

  • “f of x”
  • Input = x
  • Output = f(x) = y
  • y = 6 – 3x
  • -2
  • -1
  • 0
  • 1
  • 2
  • 12
  • 9
  • 6
  • 0
  • 3
  • x
  • y
  • f(x) = 6 – 3x
  • -2
  • -1
  • 0
  • 1
  • 2
  • 12
  • 9
  • 6
  • 0
  • 3
  • x
  • f(x)
  • Before…
  • Now…
  • (x, y)
  • (input, output)
  • (x, f(x))

Example.

  • f(x) = 2x2 – 3
  • Find f(0), f(-3), f(5).

Finding the Domain of a Function

  • When a function is defined by an equation and the domain of the function is not stated, we assume that the domain is
  • All Real Numbers
  • There will be certain cases where specific numbers cannot be included in the domain or a set of numbers cannot be included in the domain

Examples…

  • f(x) = 2x – 5
  • *there would be no restrictions on this, so the domain is All Real Numbers
  • g(x) = 1
  • x – 2
  • *a denominator cannot equal 0, so x ≠ 2. The domain is {x | x ≠ 2}
  • h(x) = √x + 6
  • *you cannot take the square root of a negative number, so x must be ≥ -6. The domain is {x | x ≥ -6}

Your Turn…Find the domain of each function

  • f(x) = x2 + 2
  • g(x) = √x – 1
  • h(x) = 1
  • x + 5

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