Given: f(x) = 3x + 11f(x)=3x+11
The function is a line in the form: y = mx + by=mx+b, where m = "slope & "b = y"-intercept" = (0, b)m=slope & b=y-intercept=(0,b)
Find Domain and Range:
By definition lines have infinite lengths. This means the domain (the valid xx values) would be infinite. Since the range (valid yy values) is dependent on the xx values, the range would also be infinite.
Domain:" "x" is all Reals, or " (-oo,oo); x is all Reals, or (−∞,∞);
Range:" "y" is all Reals, or " (-oo,oo); y is all Reals, or (−∞,∞);
Find xx-intercept:
xx-intercept is found by setting f(x) = 0:f(x)=0:
0 = 3x + 110=3x+11
-11 = 3x−11=3x
-11/3 = x−113=x
x"-intercept:"(-11/3,0)x-intercept:(−113,0)
Find yy-intercept:
yy-intercept is found by setting x = 0:x=0:
y = f(0) = 3*0 + 11 = 11y=f(0)=3⋅0+11=11
y"-intercept:"(0,11)y-intercept:(0,11)
The yy-intercept is also (0, b) = (0, 11)(0,b)=(0,11)
Find the minimum and maximum values on the interval [-5, 0][−5,0]:
This interval represents 2 xx-values. Evaluate the function with these two values to find the minimum and maximum yy-values.
f(-5) = 3*-5 + 11 = -15 + 11 = -4f(−5)=3⋅−5+11=−15+11=−4
f(0) = 3*0 + 11 = 11f(0)=3⋅0+11=11
"minimum:"(-5, -4); "maximum:"(0, 11)minimum:(−5,−4);maximum:(0,11)
