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,...