Question #4368e

1 Answer
Aug 16, 2017

Answer:

Domain:#(-oo,oo); "Range:"(-oo, oo);#
# x"-intercept:"(-11/3,0); y"-intercept:"(0,11)#
#"min:"(-5, -4); "max:"(0, 11)#

Explanation:

Given: #f(x) = 3x + 11#

The function is a line in the form: #y = mx + b#, where #m = "slope & "b = y"-intercept" = (0, b)#

Find Domain and Range:
By definition lines have infinite lengths. This means the domain (the valid #x# values) would be infinite. Since the range (valid #y# values) is dependent on the #x# values, the range would also be infinite.

Domain:#" "x" is all Reals, or " (-oo,oo); #
Range:#" "y" is all Reals, or " (-oo,oo); #

Find #x#-intercept:
#x#-intercept is found by setting #f(x) = 0:#
# 0 = 3x + 11#

#-11 = 3x#

#-11/3 = x#

# x"-intercept:"(-11/3,0)#

Find #y#-intercept:
#y#-intercept is found by setting #x = 0:#

#y = f(0) = 3*0 + 11 = 11#

#y"-intercept:"(0,11)#

The #y#-intercept is also #(0, b) = (0, 11)#

Find the minimum and maximum values on the interval #[-5, 0]#:
This interval represents 2 #x#-values. Evaluate the function with these two values to find the minimum and maximum #y#-values.

#f(-5) = 3*-5 + 11 = -15 + 11 = -4#

#f(0) = 3*0 + 11 = 11#

#"minimum:"(-5, -4); "maximum:"(0, 11)#