79.1k views
0 votes
Write a linear function f with f(-3) = -2 and f(-2) = 3.

A) f(x) = -2x + 3
B) f(x) = 2x - 3
C) f(x) = -5x + 1
D) f(x) = x + 2

1 Answer

4 votes

Final answer:

After calculating the slope of the linear function as 5 and determining the y-intercept as 13, it was found that none of the provided options match the linear function that satisfies the conditions f(-3) = -2 and f(-2) = 3. This indicates a possible mistake in the given options.

Step-by-step explanation:

To write a linear function that satisfies the given conditions — f(-3) = -2 and f(-2) = 3 — we need to determine the function's slope and y-intercept. First, we calculate the slope (m) using the two given points:


Slope (m) =
\(
\frac{f(-2) - f(-3)}{-2 - (-3)}
\) =
\(
\frac{3 - (-2)}{1}
\) =
\(
\frac{5}{1}
\) = 5

Thus, the slope of the line is 5. Next, using the slope-intercept form of a line, y = mx + b, we substitute one of the given points (-3, -2) into the equation:

-2 = 5(-3) + b

-2 = -15 + b

b = 13

Now we have both the slope and the y-intercept, so the linear function is f(x) = 5x + 13. However, among the given choices, there is no direct match. Let's test the options:

  • For option A, f(-3) = -2(-3) + 3 = 6 + 3 = 9 (does not satisfy f(-3) = -2)
  • For option B, f(-3) = 2(-3) - 3 = -6 - 3 = -9 (does not satisfy f(-3) = -2)
  • For option C, f(-3) = -5(-3) + 1 = 15 + 1 = 16 (does not satisfy f(-3) = -2)
  • For option D, f(-3) = (-3) + 2 = -1 (does not satisfy f(-3) = -2)

None of the options matches the linear function with the given conditions, suggesting a possible error in the options provided or in the calculation.

User Zpert
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.