How to find function values

To find function values is the process of evaluating the function for given values of x.

Example #1

If f(x) = x2 + 4x + 3, find function values f(0), f(-2), and f(3).

f(0) = 02 + 4(0) + 3

      = 0 + 0 + 3

      = 3

f(-2) = (-2)2 + 4(-2) + 3

      = 4 + -8 + 3

      = -4 + 3

      = -1

f(3) = (3)2 + 4(3) + 3

      = 9 + 12 + 3

      = 21 + 3

      = 4

Example #2

If g(x) = x2 + 5x - 12, find function values g(0), g(2x), and g(-2x).

g(0) = 02 + 5(0) - 12

      = 0 + 0 -12

      = -12

g(2x) = (2x)2 + 5(2x) - 12

         = 4x2 + 10x - 12

g(-2x) = (-2x)2 + 5(-2x) - 12

         = 4x2 + -10x - 12

Example #3

If h(x) = 2x2 - 4x + 3, find function values h(0), h(-3x), and g(2x+1).

h(0) = 02 - 4(0) + 3

       = 0 - 0 + 3

       = 0 - 0 + 3

       = 3

h(-3x) = (-3x)2 - 4(-3x) + 3

          = 9x2 + 12x + 3

          = 18x2 + 12x + 3 

h(2x + 1) =  (2x+1)2 - 4(2x+1) + 3

               =  (4x2 + 4x +1) - 8x - 4 + 3

               =  8x2 + 8x + 2 - 8x - 4 + 3

        = 8x2 + 1

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