Which of the following represents the range of the function f left-parenthesis x right-parenthesis equals negative 4 times x plus 1 for the domain left-brace negative 5 comma negative 1 comma 0 comma 2 comma 10 right-brace?
(1 point)
Responses
left-brace negative 39 comma negative 7 comma 1 comma 5 comma 21 right-brace
Image with alt text: left-brace negative 39 comma negative 7 comma 1 comma 5 comma 21 right-brace
left-brace negative 41 comma negative 9 comma negative 1 comma 5 comma 21 right-brace
Image with alt text: left-brace negative 41 comma negative 9 comma negative 1 comma 5 comma 21 right-brace
left-brace negative 19 comma negative 3 comma 1 comma 5 comma 21 right-brace
Image with alt text: left-brace negative 19 comma negative 3 comma 1 comma 5 comma 21 right-brace
left-brace negative 41 comma negative 9 comma negative 3 comma negative 19 right-brace
To find the range of the function f(x) = -4x + 1 for the given domain, we can substitute each value from the domain and find the corresponding output values. Let's go through the process step by step.
1. Plug in the first value from the domain, x = -5:
f(-5) = -4(-5) + 1 = 21
2. Plug in the second value from the domain, x = -1:
f(-1) = -4(-1) + 1 = 5
3. Plug in the third value from the domain, x = 0:
f(0) = -4(0) + 1 = 1
4. Plug in the fourth value from the domain, x = 2:
f(2) = -4(2) + 1 = -7
5. Plug in the fifth value from the domain, x = 10:
f(10) = -4(10) + 1 = -39
Now, we have the output values corresponding to each input value from the domain: 21, 5, 1, -7, -39.
To determine the range, we need to find the set of all possible output values. From the given output values, we can see that the range is: {-39, -7, 1, 5, 21}.
Therefore, the correct answer is:
left-brace -39 comma -7 comma 1 comma 5 comma 21 right-brace.