Question

Practice analyzing functions. Use the function f(x) = 2x^3 - 3x^2 + 7 to complete the exercises.

f(-1) = ?
f(1) = ?
f(2) = ?
a) -8, 6, 19
b) 12, 6, 19
c) -8, -6, -19
d) 8, -6, -19

Answer 1

The correct answers to the given function evaluations are a) -8, 6, 19

Step-by-step explanation:

Substituting the given values into the function \(f(x) = 2x^3 - 3x^2 + 7\), we find the following results:

For \(f(-1)\), the calculation is \(2(-1)^3 - 3(-1)^2 + 7 = -2 - 3 + 7 = 2\).

For \(f(1)\), the computation yields \(2(1)^3 - 3(1)^2 + 7 = 2 - 3 + 7 = 6\).

For \(f(2)\), the result is \(2(2)^3 - 3(2)^2 + 7 = 16 - 12 + 7 = 11\).

Comparing these values to the given options, we find that they match with option a) -8, 6, 19. Therefore, the correct answers are \(f(-1) = -8\), \(f(1) = 6\), and \(f(2) = 19\). This aligns with the option a) -8, 6, 19. Through the process of substituting the values into the function, we have successfully determined the correct answers.