The problem asks you to evaluate two functions, $f(x)$ and $g(x)$, for various values of $x$.

Given:

• Function $f(x) = 2x - 7$
• Function $g(x) = 5$

Part (a):

Find $f(3), f(2), f(1), f(0),$ and $f(-1)$.

Using the formula for $f(x) = 2x - 7$:

1. $f(3) = 2(3) - 7 = 6 - 7 = -1$
2. $f(2) = 2(2) - 7 = 4 - 7 = -3$
3. $f(1) = 2(1) - 7 = 2 - 7 = -5$
4. $f(0) = 2(0) - 7 = 0 - 7 = -7$
5. $f(-1) = 2(-1) - 7 = -2 - 7 = -9$

Part (b):

Find $g(3), g(2), g(1), g(0),$ and $g(-1)$.

Since the function $g(x) = 5$ is a constant, the value of $g(x)$ is always 5, regardless of the input $x$.

1. $g(3) = 5$
2. $g(2) = 5$
3. $g(1) = 5$
4. $g(0) = 5$
5. $g(-1) = 5$

Summary of results:

• For part (a):

  • $f(3) = -1$
  • $f(2) = -3$
  • $f(1) = -5$
  • $f(0) = -7$
  • $f(-1) = -9$

• For part (b):

  • $g(3) = 5$
  • $g(2) = 5$
  • $g(1) = 5$
  • $g(0) = 5$
  • $g(-1) = 5$

Let me know if you'd like more details or further explanations!

Here are 5 related questions to deepen your understanding:

1. How would the graph of $f(x) = 2x - 7$ look, and what are its slope and y-intercept?
2. What happens to the function $f(x)$ if we modify it to $f(x) = 3x - 7$?
3. How do you interpret a constant function like $g(x) = 5$ graphically?
4. What effect would adding a term to $g(x)$, like $g(x) = 5 + x$, have on the function's behavior?
5. Can you think of real-world examples where constant functions like $g(x) = 5$ might be useful?

Tip: Always double-check your calculations by substituting values back into the equation, especially when dealing with negative signs!