Question 23 of 25
1 answer:
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Answer:
a) P(0, <u>2</u>), Q(<u>4</u>, 0)
b) Please find attached the plot of the points P and Q on a chart made with MS Excel
c) Please find the graph of the line that represent the function 4·x + 2·y = 8 for values of x from -2 to 3 made with the Insert Chart feature on MS Excel
Step-by-step explanation:
The given equation for the line is 4·x + 2·y = 8
a) The coordinates of P = P(0, _)
Therefore, the point 'P', which is the point where the variable y = 0, is the point the (straight line) graph intercepts the x-axis (the x-intercept)
When y = 0 from the given equation, we get;
4·x + 2·y = 8
At the point y = 0;
4·x + 2 × 0 = 8
x = 8/4 = 2
x = 2
∴ The coordinates of P = P(0, _) = P(0, <u>2</u>)
Similarly, when x = 0, we get;
4·x + 2·y = 8
At the point x = 0;
4 × 0 + 2·y = 8
y = 8/2 = 4
y = 4
∴ The coordinates of Q = Q(_, 0) = Q(<u>4</u>, 0)
b) Rewriting the given equation in terms of 'y' gives;
y = (8 - 4·x)/2 = 4 - 2·x
y = 4 - 2·x
With the help of MS Excel, the points P and Q are plotted in the attached graph
c) The line of the graph of the function 4·x + 2·y = 8 for values of x from -2 to 3 can be added by Changing the Chart Type to 'Scatter with Smooth Lines and Markers' within MS Excel as presented in the included graph of the line.
Ok, first you need to read a - g and mark down the information you know. Also, this continuous function can look pretty much like anything long as it has the a - g constraints/rule.
A) We know the domain(x values) is between -10 to infinity
(-10,-9,-8,-7,-6,-5,-4,-3-,2,-1,0,1,2,3,4,5,6,7,8,9,10, to ---------> infinity)
B) We know the range(y values) is between -6 to infinity
(-6,-5,-4,-3-,2,-1,01,2,3,4,5,6,7,8,9,10, to ---------> infinity)
C) Next we know f(0) = f(4) = 0
So we know when x = 0 that f(0) = 0 or we can say y = 0. We also know when f(4) = 0 so when x = 4 y = 0. So we have two points (0,0) and (4,0) that our function will be on so plot the two points (0,0) (4,0)
D) It tells us that f(x) (y) is increasing between the x values (-10,-6) or (-2,2) or (4, to infinity)
E) It tells us that f(x) (y) is decreasing between the x values (-6,-2) or between (2,4)
F) Tells us that f(x) (y) is greater than or equal to between the x values of [-8,-4] or between the x values [0, to infinity) so this lets us know our drawing is going to be above or equal to 0 when we are in the values [-8,-4] or [0, to infinity)
G) Tells us that f(x) (y) is less than 0 when the function / drawing is between the x values of (-10, -8) or (-4,0)
The picture is what the function could look like. It can be different but needs to following the rules that are given
A) We know the domain(x values) is between -10 to infinity
(-10,-9,-8,-7,-6,-5,-4,-3-,2,-1,0,1,2,3,4,5,6,7,8,9,10, to ---------> infinity)
B) We know the range(y values) is between -6 to infinity
(-6,-5,-4,-3-,2,-1,01,2,3,4,5,6,7,8,9,10, to ---------> infinity)
C) Next we know f(0) = f(4) = 0
So we know when x = 0 that f(0) = 0 or we can say y = 0. We also know when f(4) = 0 so when x = 4 y = 0. So we have two points (0,0) and (4,0) that our function will be on so plot the two points (0,0) (4,0)
D) It tells us that f(x) (y) is increasing between the x values (-10,-6) or (-2,2) or (4, to infinity)
E) It tells us that f(x) (y) is decreasing between the x values (-6,-2) or between (2,4)
F) Tells us that f(x) (y) is greater than or equal to between the x values of [-8,-4] or between the x values [0, to infinity) so this lets us know our drawing is going to be above or equal to 0 when we are in the values [-8,-4] or [0, to infinity)
G) Tells us that f(x) (y) is less than 0 when the function / drawing is between the x values of (-10, -8) or (-4,0)
The picture is what the function could look like. It can be different but needs to following the rules that are given
