Consider the function w(x) = 10 - 13sin(4x + p)

Question

Consider the function w(x) = 10 − 13sin(4x + π)

(c) Find the minimum value. 
(d) Find the vertical intercept.

(e) Find the horizontal shift

For c I said -23 but I got it wrong and I don't know how to find any other value.

for d I said -10 but got it wrong as well

and for e I said pi units left but got it wrong.

I don't know what to do, please help me.

 

Answer 1

 C)  -1 ≤ sin (4x + π ) ≤ 1

 

     multiplying all y-values by -13 moves this point

     down to a y-value = -13

 

     Then, adding 10 to all of these y-values will move 

     the graph up 10 units

 

     your minimum y-value is -3

 

D) The vertical shift is 10 units up

 

E) The horizontal shift is found by looking at (4X + Π),

     set    (4X + π ) = 0

        4 ( X + π/4 ) = 0      you must factor to get X by itself

                         X = -Π/4

 Therefor your graph has a horizontal shift of π/4 units left

 

    

Answer 2

c) Notice that the sine value gets subtracted, so the min value is 10 - 13, using the maximum value 1 for sine

d) Vertical intercept? Not a common term. Do they mean the w intercept? If so, that's when x = 0, so just substitute.

e) The horizontal shift comes from the argument of sine being something other than just x(or a constant multiple of x).

Set the argument to zero & find out what x value that gives.  4x + pi = 0  x = -¼(pi); this means that the nominal starting value of the sine wave has been shifted left by the amount pi/4.

 

Note that I assumed that the "p"value represents pi.  If wrong, just replace my pi by p.