If you are given that y = f(x, v, w) = 2x -3 w + 5v;...

If you are given that y = f(x, v, w) = 2x -3 w + 5v; if you are also told the values of w = 5 and v = 10

a) Find an expression for f(x) = y in terms of x (i.e. plug in for w and v and reduce the equation

b) Plot your solution to the right

c) If you are told that x changes from 4 to 6, illustrate and explain what happens in your graph above.

d) If you are told that w changes from 5 to 2, how does this change what you solved/plotted? Show graphically and explain. Hint: Go back to your original equation and plug in w = 2 and v =2 and plot the line. What happened?

Solutions

Expert Solution

(a) We have the function as . Putting the values of w and v, we have or , which is the required expression such that y is a function of x.

(b) The plot is as below.

(c) If x changes from 4 to 6, we have y change from to . We have the plot as below.

As can be seen, the change occurs along or within the curve. The change occurs from point A to point B, as x increases by 2, y increased by 4.

(d) For w=2, we have the new function as or . In this case, for the same change in x from 4 to 6, we have y change from to . The plot is as below.

As can be seen, the change in w shifted the curve, and the points changed, while the change in y due to change in x is different than before. Due to the change in w, the change takes place from C to D, instead of A to B.

Rahul Sunny answered 1 year ago

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