Question

Find the range of ƒ(x) = –2x – 5 for the domain {–2, –1, 1, 2}.


{–1, –3, –7, –9}


{–1, –3, 7, 9}


{–1, –3, 3, 5}


{1, 3, 5, 7}

Answer 1

To find the range of the function \( f(x) = -2x - 5 \) for the specified domain \( \{-2, -1, 1, 2\} \), we will evaluate the function at each point in the domain.

1. For \( x = -2 \):
\[
f(-2) = -2(-2) - 5 = 4 - 5 = -1
\]

2. For \( x = -1 \):
\[
f(-1) = -2(-1) - 5 = 2 - 5 = -3
\]

3. For \( x = 1 \):
\[
f(1) = -2(1) - 5 = -2 - 5 = -7
\]

4. For \( x = 2 \):
\[
f(2) = -2(2) - 5 = -4 - 5 = -9
\]

Now, we compile the outputs:
\[
f(-2) = -1, \quad f(-1) = -3, \quad f(1) = -7, \quad f(2) = -9
\]

Thus, the range of \( f(x) \) for the given domain is:
\[
\{-1, -3, -7, -9\}
\]

Therefore, the correct answer is:
\[
\{–1, –3, –7, –9\}
\]