Answer:
-8 < x< 3
Step-by-step explanation:
|2x+5| <11
there are two solutions, one positive and one negative ( remember to flip the inequality for the negative)
2x+5 <11 and 2x+5 > -11
Subtract 5 from each side
2x+5-5 < 11-5 and 2x+5-5 > -11-5
2x< 6 and 2x>-16
Divide by 2
2x/2 <6/2 and 2x/2 >-16/2
x <3 and x>-8
-8 < x< 3
x is less than 3 and x is greater than -8
open circles and -8 and 3 and a line between
Answer:
Step-by-step explanation:
Please refer to the Image attached to this.
The Line passing through the rainbow represents the Airplane Trajectory.
2.
a) Domain and Range :
Domain is the set of values of which a function is satisfied. Range is the set of all possible output values from a function. In this problem, referring to the image attached , we can see that the , we have some or other value of y for every x . That means that, it is defined for every real value in x. Hence the Domain will be Set of all real numbers . Where as the maximum value of y we have in this problem is 36. But y has no end towards negative side. Hence the possible outcomes are from negative infinity to 36. Hence range will be (-∞,36] , where 36 is included.
Domain = R
Range = (-∞,36]
b) x and y intercepts represents the distance of points where a graph cuts the both axes from the center. Please refer to the image attached. Here we can see that for our function
X intercepts are = ±6 as they cut x axis on two points ( -6,0) and (6,0)
Y intercept = 36 as graph cuts y axis at one point (0,36)
c) The linear function will the equation of line passing through (-5,11) and (4,20)
The slope of line will be
m=1
Hence the function has a positive slope here , and hence we can say that it is a positive function.
The equation will be
y-20=x-4
d)
now we are having two equations.
i)
ii)
The solution of above two system of linear equation will be the points at which they intersect. Referring to the image attached we can see that they are intersecting at (-5,11) and (4,20) . Hence x=-5 & 4 are the solution to the system of equation we have now.
Question 3:
Please refer to the Image attached for the piece wise function
Here we have assumed two function with condition like given under
y=x+1 { x ≤ 3 }
y=4 {x > 3}
for values less than or equal to 3 , we have our function as y=x+1
let us graph this by joining two coordinates
x=0, y =1
x=1 , y= 2
x=3 , y=4
Hence we have two coordinates as (0,1) and (1,2)
we join them and limit it upto only (3,4)
because for values x>3 , the function will result us , y=4
which is a constant function , hence for every value of x . 3 , we will have 4 as output. Hence it will represent a straight line parallel to the x axis at a distance of 4 units from it.
