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)
