a is the amplitude.
b is the frequency.
c is the horizontal shift.
d is the vertical shift.
your equation is y=-2.3sin (5x)+7
the amplitude is 2.3
the frequency is 5
the vertical displacement is 7
the period is equal to 360 degrees / the frequency.
that makes the period equal to 360 / 5 = 72 degrees.
since the vertical displacement is 7, the center line of the sine wave is at y = 7.
this makes the range of the sine wave equal to 7 - 2.3 to 7 + 2.3.
that makes it equal to 4.7 <= y <= 9.3.
the domain is all real values of x, since there are no restrictions on the value of x.
that makes the domain - infinity < x < + infinity.
all this was done without graphing.
however, to confirm whether the information supplied is correct, i drew some graphs that are shown below.
the graph confirms what i gold you up top.
the period is 72 degrees.
the frequency is 5
the amplitude is 2.3
the range is y = 4.7 to 9.3
the center line is y = 7
the domain is all real values of x.
the sine wave repeats every 72 degrees.
the domain would be 0 <= x <= 72 plus or minus k * 72, where k is a positive integer.
that makes the domain all real values of x because the value of x goes infinitely on to the right or to the left of the basic period of 0 to 72 degrees.