Answer:
Step-by-step explanation:
Graph: f(x) = 1 - ex
You meant f(x) = 1 - e^x, where ^ represents exponentiation.
First, graph the parent function y = e^x. The y-intercept of this graph is (0, 1), and the x-axis is the horizontal intercept. The graph begins on the left in Quadrant 2 and continues upward in Quadrant 1.
Next, reflect this graph in the x-axis, due to the - sign in f(x) = 1 - e^x. The y-intercept is (0, -1) and the horizontal asymptote is the x-axis.
Finally, translate the whole graph upward by 1 unit.
Answer:
21+35
Step-by-step explanation:
use distributive property, multiply 7 by the two numbers in the parenthesis
keep the problem though.
Answer:
The range of this set of numbers is 9
Step-by-step explanation:
The range is the greatest number subtracted by the lowest number
in this problem that is 21-12
Step-by-step explanation:
a). A = {x ∈ R I 5x-8 < 7}
5x - 8 < 7 <=> 5x < 8+7 <=> 5x < 15 =>
x < 3 => A = (-∞ ; 3)
A ∩ N = {0 ; 1 ; 2}
A - N* = (-∞ ; 3) - {1 ; 2}
b). A = { x ∈ R I 7x+2 ≤ 9}
7x+2 ≤ 9 <=> 7x ≤ 7 => x ≤ 1 => x ∈ (-∞ ; 1]
A ∩ N = {0 ; 1}
A-N* = (-∞ ; 1)
c). A = { x ∈ R I I 2x-1 I < 5}
I 2x-1 I < 5 <=> -5 ≤ 2x-1 ≤ 5 <=>
-4 ≤ 2x ≤ 6 <=> -2 ≤ x ≤ 3 => x ∈ [-2 ; 3]
A ∩ N = {0 ; 1 ; 2 ; 3}
A - N* = [-2 ; 3) - {1 ; 2}
d). A = {x ∈ R I I 6-3x I ≤ 9}
I 6-3x I ≤ 9 <=> -9 ≤ 6-3x ≤ 9 <=>
-15 ≤ -3x ≤ 3 <=> -5 ≤ -x ≤ 3 =>
-3 ≤ x ≤ 5 => x ∈ [-3 ; 5]
A ∩ N = {0 ; 1 ; 2 ; 3 ; 4 ; 5}
A - N* = [-3 ; 5) - {1 ; 2 ; 3 ; 4}
