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2 answers:
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The domain of the function is all real numbers except 2 and -1
Step-by-step explanation:
Domain is the set of inputs of a function on which the function is defined.
Given function is:
In case of a function involving fraction, the function is undefined if the denominator is zero so in order to find the domain of the function algebraically , we have to find the values on which the function will be undefined
The function will be undefined on x=-1 and x=2
So,
The domain of the function is all real numbers except 2 and -1
Keywords: Domain, functions
Learn more about domain and functions at:
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Answer:
1. -2/3 3. -5/4 5. 3/2 FOR THE REST OF THE PARTS LOOK THROUGH THE EXPLANATIONS
Step-by-step explanation:
Before I start the workings, I'll give a little explanation on this topic.
So, the equation of a straight line is
y = mx + c
where x and y are any coordinates of any point on the line.
m is the gradient or slope
m can be calculated using 2 formulas,
formula 1: Rise/Run
where rise is the how much a graph goes upwards or downwards, if its upwards use positive integer and if its downwards use negative integer.
Run is how much a graph moves to the right or to the left, if it moves to the right is is positive, if it moves to the left it is negative.
Formula 2: (y2-y1)/(x2-x1)
the values of these are taken through any 2 coordinates on the line.
and c is the y-intercept(the point where the line crosses the y-axis.
<u>MOVING TO ANSWERING NOW</u>
1. Dotted points on the line are (1,0) and (4,-2)
Formula of slope,
U can use any of the 2 formulas given above
I'll show both for this question
m = (y2-y1)/(x2-x1) = (-2-0)/(4-1) = -2/3
OR
m = rise/run = where rise is -2 and run is 3 so -2/3
2. TRY DOING THIS ONE YOURSELF
For the next part I'll do 3 and 5 for your understanding, try doing 2 and 4 on your own to understand.
3. Coordinates given (13,1) and (1,16)
m = (y2-y1)/(x2-x1) = (16-1)/(1-13) = 15/-12 simplify this and it becomes -5/4
5. (-8,-14) and (-10,-17)
m = (y2-y1)/(x2-x1) = (-17-(-14))/(-10-(-8)) = -3/-2 = 3/2
FOR THE NEXT PART I'LL DO 7,8 AND 10 FOR YOU, TRY DOING 9 ON YOUR OWN FOR PRACTICE.
I WILL ALSO ATTACH FILES FOR THE NEXT PARTS IN ORDER OF QUESTIONS SO SEE THEM.
7. y = x + 3 this means y = 1x +3 which means:
1 is the gradient
3 is the y-intercept
so 1 as a fraction is 1/1 which means rise is one upwards and run is 1 to the right.
Now go to the graph on the y-axis and plot the point 3, (0,3) is your y-intercept. From their rise by one and run by one this will lead u to point (1,4)
Mark both these points and make a line through them.
8. x = -5
now look at this equation in the form of y = mx + c
0 = 1x + 5 the means y is 0 and it is already told in the question that x = -5
if u rearrange 0 = 1x + 5 it will give you x = -5
now when y is 0 x = -5 put a point on the coordinate (-5,0) and draw a vertical straight line.
10. y = (1/4)x - 1
slope is 1/4 which means rise is 1 and run is 4
y-intercept is -1
now go to y=-1 which is the coordinate (0,-1) and rise by one and run by 4, this will take u to the coordinate (4,0) now put a dot on both coordinates, connect them and put a line through them.
