Sure! Let's evaluate the function [tex]\( f(x) = x^2 - 4 \)[/tex] at the given points step-by-step.
(a) To find [tex]\( f(3) \)[/tex]:
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex].
2. [tex]\( f(3) = 3^2 - 4 \)[/tex]
3. Calculate the square: [tex]\( 3^2 = 9 \)[/tex]
4. Subtract 4 from 9: [tex]\( 9 - 4 = 5 \)[/tex]
Thus, [tex]\( f(3) = 5 \)[/tex].
(b) To find [tex]\( f(-4) \)[/tex]:
1. Substitute [tex]\( x = -4 \)[/tex] into the function [tex]\( f(x) \)[/tex].
2. [tex]\( f(-4) = (-4)^2 - 4 \)[/tex]
3. Calculate the square: [tex]\( (-4)^2 = 16 \)[/tex]
4. Subtract 4 from 16: [tex]\( 16 - 4 = 12 \)[/tex]
Thus, [tex]\( f(-4) = 12 \)[/tex].
(c) To find [tex]\( f(0) \)[/tex]:
1. Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) \)[/tex].
2. [tex]\( f(0) = 0^2 - 4 \)[/tex]
3. Calculate the square: [tex]\( 0^2 = 0 \)[/tex]
4. Subtract 4 from 0: [tex]\( 0 - 4 = -4 \)[/tex]
Thus, [tex]\( f(0) = -4 \)[/tex].
(d) To find [tex]\( f(-2) \)[/tex]:
1. Substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( f(x) \)[/tex].
2. [tex]\( f(-2) = (-2)^2 - 4 \)[/tex]
3. Calculate the square: [tex]\( (-2)^2 = 4 \)[/tex]
4. Subtract 4 from 4: [tex]\( 4 - 4 = 0 \)[/tex]
Thus, [tex]\( f(-2) = 0 \)[/tex].
Summarizing the results:
- [tex]\( f(3) = 5 \)[/tex]
- [tex]\( f(-4) = 12 \)[/tex]
- [tex]\( f(0) = -4 \)[/tex]
- [tex]\( f(-2) = 0 \)[/tex]
