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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]
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}.
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:
Hence the range is given by:
{-52, -36, -12, 20, 68}.
For function b, the numeric values are given by:
Hence the range is given by:
{-293, -68, -41, -5, 7}.
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