Respuesta :

The range of the function f(x) = 8x - 12 over the interval [-5, -2, 0, 4, 10] is [-52, -28, -12, 20, 68]. The range of the function g(x) = -3x² + 7 over the interval [-5, -2, 0, 4, 10] is [-68, -5, 7, -41, -293]

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Given that:

f(x) = 8x - 12

f(-5) = 8(-5) - 12 = -52

f(-2) = 8(-2) - 12 = -28

f(0) = 8(0) - 12 = -12

f(4) = 8(4) - 12 = 20

f(10) = 8(10) - 12 = 68

g(x) = -3x² + 7

g(-5) = -3(-5)² + 7 = -68

g(-2) = -3(-2)² + 7 = -5

g(0) = -3(0)² + 7 = 7

g(4) = -3(4)² + 7 = -41

g(10) = -3(10)² + 7 = -293

The range of the function f(x) = 8x - 12 over the interval [-5, -2, 0, 4, 10] is [-52, -28, -12, 20, 68]. The range of the function g(x) = -3x² + 7 over the interval [-5, -2, 0, 4, 10] is [-68, -5, 7, -41, -293]

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Considering the given domains of the function, the ranges are given by:

a) {-52, -36, -12, 20, 68}.

b) {-293, -68, -41, -5, 7}.

What is the range of a function?


The range of a function is composed by the set that contains all output values corresponding to the input values(domain) for the function.

For function a, the numeric values are given by:

  • f(-5) = 8(-5) - 12 = -40 - 12 = -52.
  • f(-2) = 8(-2) - 12 = -24 - 12 = -36.
  • f(0) = 8(0) - 12 = 0 - 12 = -12.
  • f(4) = 8(4) - 12 = 32 - 12 = 20.
  • f(10) = 8(10) - 12 = 80 - 12 = 68.

Hence the range is given by:

{-52, -36, -12, 20, 68}.

For function b, the numeric values are given by:

  • g(-5) = -3(-5)² + 7 = -3 x 25 + 7  = -68.
  • g(-2) = -3(-2)² + 7 = -3 x 4 + 7  = -5.
  • g(0) = -3(0)² + 7 = -3 x 0 + 7  = 7.
  • g(4) = -3(4)² + 7 = -3 x 16 + 7  = -41.
  • g(10) = -3(10)² + 7 = -3 x 100 + 7  = -293.

Hence the range is given by:

{-293, -68, -41, -5, 7}.

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