- Submitted By: cairajillian
- Date Submitted: 01/22/2014 6:30 PM
- Category: Miscellaneous
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Chapter 5 review solutions

1) fx=x-52(x-3)

a) List each x-intercept (zero) and its multiplicity (round to 2 decimal places when needed)

(x-5)2(x-3) = 0

(x-5)(x-5)(x-3)=0

x – 5 = 0 or x – 3 = 0

x = 5 or x = 3

Answer: (5,0) even multiplicity, (3,0) odd multiplicity

b) Determine whether the graph crosses or touches the x-axis at each x-intercept

Answer: graph touches x-axis at (5,0) graph crosses x-axis at (3,0)

c) Determine the maximum number of turning points on the graph

Multiply the first in the expanded polynomial to get x*x*x = x3, this is a third degree polynomial.

Answer: will have at most 2 turning points

d) Which function will the graph of f(x) behave like for large values of x

Answer: graph will behave like f(x) = x3 for large values of x.

e) Describe the end behavior

Answer: falls to the left, rises to the right

f) sketch a graph and approximate the turning points, also label the x-intercepts

)

g) state the intervals where the function is increasing and decreasing

answer: increasing (-∞,3.67) ∪(5,∞) decreasing (3.67, 5)

2) fx=(x2-16)(3x-21)

a) List each x-intercept (zero) and its multiplicity (round to 2 decimal places when needed)

(x2 - 16)(3x – 21) = 0

(x+4)(x-4)(3x-21) = 0

x+ 4 = 0 x – 4 = 0 3x – 21 = 0

x = -4 x = 4 x = 7

Answer: (-4,0) odd mult (4,0) odd mult (7,0) odd mult

b) Determine whether the graph crosses or touches the x-axis at each x-intercept

Answer: crosses at (-4,0) crosses at ( 4,0) crosses at ( 7,0)

c) Determine the maximum number of turning points on the graph

multiply the firsts in the expanded problem x2*3x = 3x3

this is a 3rd degree polynomial

Answer: will have at most 2 turning points.

d) Which function will the graph of f(x) behave like for large values of x

Answer: will behave like f(x) = 3x3

e) Describe the end behavior

Answer: fall left and rises to the right

f) sketch a graph and approximate the turning points,...