For the linear function [tex]f(x) = 7x - 4[/tex], find the range of [tex]f(x)[/tex] at [tex]x = -2, 0[/tex], and [tex]2[/tex].

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]



Answer :

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]