Check?
25. f(x)= x^2-1 ; -3, -2, -1, 0, 1, 2 ,3
=
f(x); -3^2-1=-10
f(x) ; -2^2-1=-5
f(x) ; -1^2-1=-2
f(x) ; 0^2-1=-1
f(x) ; 1^2-1=0
f(x) ; 2^2-1=3
f(x) ; 3^2-1=8
26. g(x); √(x+1)-2 ; x+-1, 0, 3, 8
g(x) ; √(-1+1)-2=-2
g(x) ; √(0+1)-2=-1
g(x) ; √(3+1)-2=4
g(x) ; √(8+1)-2=1
27. h(x)= |x-3| ; x=0,1,2,3,4,5,6
h(x); |0-3| =3
h(x); |1-3|=4
h(x); |2-3|=5
h(x); |4-3|=7
h(x); |5-3|=8
h(x); |6-3|=9
25.
all squares are positive
thus f(-3) = (-3)^2-1 = 9-1 = 8
-3^2 = -9, but (-3)^2 = +9
when substituting in for x, to avoid mistakes, always enclose the value in ().
26.
f(3) = √(3+1)-2 = √4 - 2 = 2-2 = 0
27.
|x| = -x if x<0
|x| = x if x >= 0
so, |1-3| = |-2| = 2, not 4
do the addition first, then the ||.
Treat the || like special parentheses, or treat |x| like a function abs(x), so all the inside stuff is done first
|1-3| = 2
|1| + |-3| = 1+3 = 4
Based on the given functions and values, let's find the corresponding outputs for each input:
For f(x) = x^2 - 1:
- When x = -3, substituting the value: f(-3) = (-3)^2 - 1 = 9 - 1 = 8
- When x = -2, substituting the value: f(-2) = (-2)^2 - 1 = 4 - 1 = 3
- When x = -1, substituting the value: f(-1) = (-1)^2 - 1 = 1 - 1 = 0
- When x = 0, substituting the value: f(0) = (0)^2 - 1 = -1
- When x = 1, substituting the value: f(1) = (1)^2 - 1 = 1 - 1 = 0
- When x = 2, substituting the value: f(2) = (2)^2 - 1 = 4 - 1 = 3
- When x = 3, substituting the value: f(3) = (3)^2 - 1 = 9 - 1 = 8
For g(x) = √(x + 1) - 2:
- When x = -1, substituting the value: g(-1) = √(-1 + 1) - 2 = √0 - 2 = -2
- When x = 0, substituting the value: g(0) = √(0 + 1) - 2 = √1 - 2 = -1
- When x = 3, substituting the value: g(3) = √(3 + 1) - 2 = √4 - 2 = 0
- When x = 8, substituting the value: g(8) = √(8 + 1) - 2 = √9 - 2 = 1
For h(x) = |x - 3|:
- When x = 0, substituting the value: h(0) = |0 - 3| = |-3| = 3
- When x = 1, substituting the value: h(1) = |1 - 3| = |-2| = 2
- When x = 2, substituting the value: h(2) = |2 - 3| = |-1| = 1
- When x = 3, substituting the value: h(3) = |3 - 3| = |0| = 0
- When x = 4, substituting the value: h(4) = |4 - 3| = |1| = 1
- When x = 5, substituting the value: h(5) = |5 - 3| = |2| = 2
- When x = 6, substituting the value: h(6) = |6 - 3| = |3| = 3
Therefore, the complete evaluation of the given functions for the given values is as follows:
f(x): -10, -5, -2, -1, 0, 3, 8
g(x): -2, -1, 4, 1
h(x): 3, 2, 1, 0, 1, 2, 3