Given the function
[tex]y=\dfrac{3}{5}x+2[/tex]
and its domain [tex]\{-10,0,5\}[/tex], its range is [tex]\{-4,2,5\}[/tex]
The domain of a function is the set of all possible values that we can input to the function.
The range of a function is the set of all possible values that a function can output.
For the function
[tex]y=\dfrac{3}{5}x+2[/tex]
if the domain is the set [tex]\{-10,0,5\}[/tex], we can get the range by substituting each value in the domain into the function. The resulting set of values gives the range of the function.
The range will then be
[tex]\left\{\dfrac{3}{5}(-10)+2, \dfrac{3}{5}(0)+2,\dfrac{3}{5}(5)+2\right\}\\\\=\left\{3(-2)+2, 3(0)+2, 3(1)+2\right\}\\\\=\left\{-4, 2, 5\right\}\\\\[/tex]
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