How to find function values

To find function values is the process of evaluating the function for given values of x. The figure below shows how to evaluate f(x) = 6x - 5 when x  = 2. 

More examples showing how to find function values

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) = 2×0² - 4(0) + 3

       = 2×0 - 0 + 3

       = 0 - 0 + 3

       = 3

h(-3x) = 2×(-3x)² - 4(-3x) + 3

          = 2×9x² + 12x + 3

          = 18x² + 12x + 3 

h(2x + 1) =  2×(2x+1)² - 4(2x+1) + 3

               =  2×(4x² + 4x +1) - 8x - 4 + 3

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

       = 8x² + 1

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