Answer:
a) (0.555, 0) and (6, 0)
b) r = -3 and r = 1.8
c) (0.875, 0.676)
d) (0, 1.235)
Step-by-step explanation:
Set each term in the numerator and denominator equal to 0 and find r.
In the numerator:
r = 7/8, 5/9, or 6
In the denominator:
r = 9/5, 7/8, or -3
Zeros in the numerator that aren't in the denominator are r-intercepts.
Zeros in the denominator that aren't in the numerator are vertical asymptotes.
Zeros in both the numerator and the denominator are holes.
a) (0.555, 0) and (6, 0)
b) r = -3 and r = 1.8
c) Evaluate m(r) at r = 7/8. To do that, first divide out the common term (-8r + 7) from the numerator and denominator.
m(r) = (-9r+5)² (r−6)² / ( (-5r+9)² (r+3)² )
m(⅞) = (-9×⅞+5)² (⅞−6)² / ( (-5×⅞+9)² (⅞+3)² )
m(⅞) = (-23/8)² (-41/8)² / ( (37/8)² (31/8)² )
m(⅞) = (-23)² (-41)² / ( (37)² (31)² )
m(⅞) = 0.676
The hole is at (0.875, 0.676).
d) Evaluate m(r) at r = 0.
m(0) = (-9×0+5)² (0−6)² / ( (-5×0+9)² (0+3)² )
m(0) = (5)² (-6)² / ( (9)² (3)² )
m(0) = 1.235
The m(r)-intercept is (0, 1.235).
