Question

(3 points)
Use the function f(x)=2x3−3x2+7
to complete the exercises.

f(−1)=


f(1)=


f(2)=

Answer 1

To evaluate the function \( f(x) = 2x^3 - 3x^2 + 7 \) at the specified values, we will substitute each value of \( x \) into the function.

1. **Calculate \( f(-1) \)**:
\[
f(-1) = 2(-1)^3 - 3(-1)^2 + 7
\]
\[
= 2(-1) - 3(1) + 7
\]
\[
= -2 - 3 + 7
\]
\[
= 2
\]

2. **Calculate \( f(1) \)**:
\[
f(1) = 2(1)^3 - 3(1)^2 + 7
\]
\[
= 2(1) - 3(1) + 7
\]
\[
= 2 - 3 + 7
\]
\[
= 6
\]

3. **Calculate \( f(2) \)**:
\[
f(2) = 2(2)^3 - 3(2)^2 + 7
\]
\[
= 2(8) - 3(4) + 7
\]
\[
= 16 - 12 + 7
\]
\[
= 11
\]

So, the values are:
- \( f(-1) = 2 \)
- \( f(1) = 6 \)
- \( f(2) = 11 \)