Your answers to parts a, b & d are correct but as for answer c) it is 4 /3 to the left, as 4sin(2x + 4 /3) -5
To make the graph of this function:
1. First make a dotted at the mean position i.e y= -5
2. Mark with dotted line the amplitude i.e on y= -1 and -9
3. Now mark the point -2 /3,-5 (you can check sin [2 ( x+(2 /3)] to be zero at this -2 /3)
4. Now starting from the point(-2 /3,-5) ,taking y=-5 as the mean position line and considering the limits i.e amplitude in step 2, draw the graph quite similar to sin(0.5x). Add to -2 /3 to get the point on x-coordinate where one complete cycle ends.
For part f) there will be no x-intercepts because max. value of this function is -1.