find the range given the following domain. f(x)=-5x+3; {-2,-1,0,1,2}

To find the range of the function \( f(x) = -5x + 3 \) for the given domain \( \{-2, -1, 0, 1, 2\} \), we will evaluate the function at each value of \( x \).

1. For \( x = -2 \):
   \[
   f(-2) = -5(-2) + 3 = 10 + 3 = 13
   \]

2. For \( x = -1 \):
   \[
   f(-1) = -5(-1) + 3 = 5 + 3 = 8
   \]

3. For \( x = 0 \):
   \[
   f(0) = -5(0) + 3 = 0 + 3 = 3
   \]

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

5. For \( x = 2 \):
   \[
   f(2) = -5(2) + 3 = -10 + 3 = -7
   \]

Thus, the range of the function for the given domain \( \{-2, -1, 0, 1, 2\} \) is:

\[
\{13, 8, 3, -2, -7\}
\]

### Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What is the slope of the function \( f(x) = -5x + 3 \)?
2. How does changing the domain affect the range of a function?
3. How would the range change if the function was \( f(x) = 5x + 3 \) instead?
4. What is the meaning of the y-intercept in the function \( f(x) = -5x + 3 \)?
5. How can you graph the function based on the calculated points?

**Tip:** In linear functions, the slope determines how fast the function increases or decreases as \( x \) changes.

Find the range given the following domain. f(x)=-5x+3; {-2,-1,0,1,2}

Discover how to find the range of the linear function f(x) = -5x + 3 for the domain {-2,-1,0,1,2}. This problem explores algebraic concepts related to linear functions and teaches how to calculate the range from a given domain, suitable for students in Grades 8-10.

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