To solve the problem of finding the values of the function [tex]\( f(x) = 7x - 4 \)[/tex] at specific points [tex]\( x = -2 \)[/tex], [tex]\( x = 0 \)[/tex], and [tex]\( x = 2 \)[/tex], we will evaluate the function at these points one by one.
1. Finding [tex]\( f(-2) \)[/tex]:
[tex]\[
f(-2) = 7(-2) - 4
\][/tex]
Calculate the expression:
[tex]\[
f(-2) = -14 - 4
\][/tex]
[tex]\[
f(-2) = -18
\][/tex]
2. Finding [tex]\( f(0) \)[/tex]:
[tex]\[
f(0) = 7(0) - 4
\][/tex]
Calculate the expression:
[tex]\[
f(0) = 0 - 4
\][/tex]
[tex]\[
f(0) = -4
\][/tex]
3. Finding [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = 7(2) - 4
\][/tex]
Calculate the expression:
[tex]\[
f(2) = 14 - 4
\][/tex]
[tex]\[
f(2) = 10
\][/tex]
The calculated values for the function at the given points are:
- [tex]\( f(-2) = -18 \)[/tex]
- [tex]\( f(0) = -4 \)[/tex]
- [tex]\( f(2) = 10 \)[/tex]
We now match these results to the given options:
- A) [tex]\( f(-2) = 10, f(0) = -4, f(2) = -18 \)[/tex]
- B) [tex]\( f(-2) = -18, f(0) = 4, f(2) = 10 \)[/tex]
- C) [tex]\( f(-2) = -18, f(0) = -4, f(2) = 10 \)[/tex]
- D) [tex]\( f(-2) = 18, f(0) = -4, f(2) = 10 \)[/tex]
The correct answer is:
C) [tex]\( f(-2) = -18, f(0) = -4, f(2) = 10 \)[/tex]
