pg. 149 homework pg. 149#2 – 23 (every 3 rd problem) pg. 151# 50 - 57 #1[-5, 5] by [-2, 10] #4[-4,...
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Pg. 149 Homework• Pg. 149 #2 – 23 (every 3rd problem)
Pg. 151 # 50 - 57
• #1 [-5, 5] by [-2, 10]• #4 [-4, 4] by [-10, 10] • #7 [-1,000, 3,000] by [-15,000,000, 2,000,000]• #10 minimum = (3/14, 831/28)• #13 Zeros = maximum = (0, 10)• #16 Intercept = (1.30, 0) and no maxima• #19 Zeros = (3.81, 0) Max = (0.33, -29.85)
Min = (1, -30)• #22 Zeros = (0, 0), (4, 0), (22, 0) Max = (1.79, 145,74)
Min = (8.21, -385.74)
10,0 , 10,0
3.1 Graphs of Polynomial Functions
Definition • A polynomial function is
one that can be written in the form:
where n is a nonnegative integer and the coefficients are real numbers. If the leading coefficient is not zero, then n is the degree of the polynomial.
State whether the following are polynomials. If so, state the degree.
11 1 0...n n
n nf x a x a x a x a
27
3f x x
3 2 1f x x x x
5 4 3 22 3 5 4 10f x x x x x
2 1f x x
121f x x x x
3.1 Graphs of Polynomial Functions
End Behavior• End behavior is determined
by the degree and the leading coefficient.
• Create Chart.
Number of “Bumps”• The number of “bumps” a
graph may have is no more than one less than the degree.
• The number of zeros a graph may have is no more than the number of the degree.
2 3 10f x x x
4 3 22 3 3f x x x x
2.7 Inverse Functions
Inverse Functions• Show that f(x) =
will have an inverse function. – Find the inverse function and
state its domain and range. – Prove that the two are
actually inverses.
• Show that g(x) = will have an inverse function. – Find the inverse function and
state its domain and range. – Prove that the two are
actually inverses.
• Will h(x) = x2 – 2xwill have an inverse function?
3 1x 2
1x
2.6 Relations and Parametric Equations
Circles• Write the following
equation of a circle in standard form and state the center and radius.
Symmetry• Determine the type of
symmetry, if any, of the equations below.
2 2 6 8 0x y x y 3 3 4xy x y
3 5f x x x
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