Question

Find the range of domain {-3,-1,1,2}
Function g(x)=x^2 -3
Options
{6,-2,1}
{-6,-2,-1}
{-12,-4,1,4}
{-4,-2,1,4}

Answer 1

To find the range of the function \( g(x) = x^2 - 3 \) for the given domain \(\{-3, -1, 1, 2\}\), we need to calculate the values of \( g(x) \) for each \( x \) in the domain.

1. For \( x = -3 \):
\[
g(-3) = (-3)^2 - 3 = 9 - 3 = 6
\]

2. For \( x = -1 \):
\[
g(-1) = (-1)^2 - 3 = 1 - 3 = -2
\]

3. For \( x = 1 \):
\[
g(1) = (1)^2 - 3 = 1 - 3 = -2
\]

4. For \( x = 2 \):
\[
g(2) = (2)^2 - 3 = 4 - 3 = 1
\]

Now, we can compile the outputs we calculated:

- For \( x = -3 \), \( g(-3) = 6 \)
- For \( x = -1 \), \( g(-1) = -2 \)
- For \( x = 1 \), \( g(1) = -2 \)
- For \( x = 2 \), \( g(2) = 1 \)

The outputs, or the range of \( g \) over the specified domain, would thus be:
\[
\{6, -2, -2, 1\}
\]
Which simplifies to:
\[
\{6, -2, 1\}
\]

Now, comparing the outputs with the given options:
1. \{6, -2, 1\} (This matches our range)
2. \{-6, -2, -1\}
3. \{-12, -4, 1, 4\}
4. \{-4, -2, 1, 4\}

The correct option for the range of the function \( g(x) \) is:
\(\{6, -2, 1\}\)