To find the Range of this function, we can substitute each value in the Domain for #color(red)(x)# and calculate the result:
For #x = -1#:
#f(color(red)(x)) = -4.7color(red)(x) + 1# becomes:
#f(color(red)(-1)) = (-4.7 xx color(red)(-1)) + 1#
#f(color(red)(-1)) = 4.7 + 1#
#f(color(red)(-1)) = 5.7#
For #x = 3#:
#f(color(red)(x)) = -4.7color(red)(x) + 1# becomes:
#f(color(red)(3)) = (-4.7 xx color(red)(3)) + 1#
#f(color(red)(3)) = -14.1 + 1#
#f(color(red)(3)) = -13.1#
For #x = 5#:
#f(color(red)(x)) = -4.7color(red)(x) + 1# becomes:
#f(color(red)(5)) = (-4.7 xx color(red)(5)) + 1#
#f(color(red)(5)) = -23.5 + 1#
#f(color(red)(5)) = -22.5#
For #x = 8#:
#f(color(red)(x)) = -4.7color(red)(x) + 1# becomes:
#f(color(red)(8)) = (-4.7 xx color(red)(8)) + 1#
#f(color(red)(8)) = -37.6 + 1#
#f(color(red)(8)) = -36.6#
The Range of #f(x)# is: #{3, -13.1, -22.5, -36.6}#
