Respuesta :
Answer:
{ 5, 17, 45 }
Step-by-step explanation:
To find the range substitute the values from the domain into p(x)
p(- 2) = 2(- 2)² - 2(- 2) + 5 = 2(4) + 4 + 5 = 8 + 4 + 5 = 17
p(0) = 2(0)² - 2(0) + 5 = 0 + 0 + 5 = 5
p(1) = 2(1)² - 2(1) + 5 = 2 - 2 + 5 = 5
p(5) = 2(5)² - 2(5) + 5 = 2(25) - 10 + 5 = 50 - 10 + 5 = 45
Range is { 5, 17, 45 } ← note 5 is only entered once
Let's plug the values into the equation:
[tex]\begin{array}{c|c|c}x&f(x)=2x^2-2x+5&\text{value}\\-2&2(-2)^2-2\cdot(-2)+5&17\\0&2(0)^2-2\cdot 0 + 5&5\\1&2(1)^2-2\cdot 1 + 5&5\\5&2(5)^2-2\cdot 5 + 5&45\end{array}[/tex]
So, the range is the set composed by the numbers
[tex]\{5,\ 17,\ 45\}[/tex]
