Alright, let’s tackle each part of the question step-by-step. We are given the function [tex]\( f(x) = 3x - 7 \)[/tex] and are asked to evaluate it at several points.
Step-by-Step Solution:
### Part a: [tex]\( f(0) \)[/tex]
To find [tex]\( f(0) \)[/tex]:
1. Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(0) = 3(0) - 7
\][/tex]
2. Simplify the expression:
[tex]\[
f(0) = 0 - 7 = -7
\][/tex]
So, the correct choice is:
A. [tex]\( f(0) = -7 \)[/tex]
### Part b: [tex]\( f(3) \)[/tex]
To find [tex]\( f(3) \)[/tex]:
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = 3(3) - 7
\][/tex]
2. Simplify the expression:
[tex]\[
f(3) = 9 - 7 = 2
\][/tex]
### Part c: [tex]\( f(-2) \)[/tex]
To find [tex]\( f(-2) \)[/tex]:
1. Substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-2) = 3(-2) - 7
\][/tex]
2. Simplify the expression:
[tex]\[
f(-2) = -6 - 7 = -13
\][/tex]
### Part d: [tex]\( f\left(\frac{1}{3}\right) \)[/tex]
To find [tex]\( f\left(\frac{1}{3}\right) \)[/tex]:
1. Substitute [tex]\( x = \frac{1}{3} \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f\left(\frac{1}{3}\right) = 3\left(\frac{1}{3}\right) - 7
\][/tex]
2. Simplify the expression. Since [tex]\( 3 \times \frac{1}{3} = 1 \)[/tex], we have:
[tex]\[
f\left(\frac{1}{3}\right) = 1 - 7 = -6
\][/tex]
So, to summarize the results:
- (a) [tex]\( f(0) = -7 \)[/tex]
- (b) [tex]\( f(3) = 2 \)[/tex]
- (c) [tex]\( f(-2) = -13 \)[/tex]
- (d) [tex]\( f\left(\frac{1}{3}\right) = -6 \)[/tex]
