Download b) y=6 4x 12

Notes #3-___
Date:______
11-6 Graphing Square Root Functions (614)
independent
variable (x)
must be in
the radicand
Square root parent function:
f(x) = x
radicand ≥ 0
Ex.1 Find the domain of each function.
a) y = x+5
b) y=6 4x!12
x
0
1
2
4
6
9
y
0
1
1.4
2
2.4
3
Ex.2 The size of a television screen is the length of the
screen’s diagonal d in inches. The equation
y= 2A estimates the length of a diagonal of a television with
screen area A. Graph the function.
Transformations:
* dilations: stretching or shrinking a graph
* reflections: flip over a line (usually axis)
* translations: sliding a graph left, right, up or down
y= x +k translates
y= x !k translates
y= x up k units
y= x down k units
Ex.3 Graph y= x and the vertical translations.
a) y= x +4
b) y= x !2
y = x+h translates
y = x!h translates
y= x to the left h units
y= x to the right h units
Ex.4 Graph y= x and the horizontal translations.
a) y = x+3
b) y = x!1
Ex.5 Graph and give the domain and range:
a) y = x !1
b) y = x +2
c) y = !3 + x !1
Summary:
Notes #3-___
Date:______
11-5 Solving Radical Equations (607)
W.1 Simplify the expressions:
a) 5 6 ! 9 6
b) 3 17 + 9 11 + 17
7! 3
c)
e)
W.2
(
3+4
d)
)
2
f)
(
2 7 3+ 2
)
5
8! 6
Find the domain of the square root functions.
a) y= x+7
b) y= x !5
Ex.1 Solve (isolate the radical and square both sides):
a) x !10 = 0
b) 3x+1 ! 2 = 6
c)
4x!3 = x
d)
x+9=0
e)
x+6 = ! x
f)
5y+6 = 2y
On a roller coaster ride, your speed in a loop depends on the
height of the hill you have just come down and the radius of
the loop in feet. The equation v=8! h!2r gives the
velocity v in feet per second of a car at the top of the loop.
Ex.2 The loop on a roller coaster ride has a radius of 18ft.
Your car has a velocity of 120 ft/s at the top of the loop.
How high is the hill you have just come down before
going into the loop?
When there are radical expressions on both sides of an
equation, square both sides.
Ex.3 Solve each equation.
a) 3x!4 = 2x+3
b) x!2 = 3x!1
Extraneous solution: solution that does not satisfy the
original equation
x = 2 ! (x)2 = (2)2 ! x 2 = 4 ! x = 2,"2
Ex.4 Solve and identify extraneous solutions.
a) x= x+12
b) x= x+2
If all solutions are
extraneous, how
many solutions does
the original equation
have?
Summary:
Ex.5 Solve each equation and check the solution(s).
a) 3x +8=2
b) 5! 2n =13
Notes #3-___
Date:______
11-7 Trigonometric Ratios (621)
W.1 Solve 6r!3= 3r+6
W.2
Are (1, 3), (-2, 3) & (1, 1) vertices of a right triangle?
W.3
Find the midpoint of (-9,-1) and (4,11).
What is trigonometry?
B
Opposite
Hypotenuse
Adjacent
Adjacent
A
Hypotenuse
Opposite
The opposite side depends on which angle is used.
The hypotenuse is never the opposite or adjacent side.
Mnemonic device.
SOH CAH TOA
sinA =
opposite
hypotenuse
cosA =
adjacent
hypotenuse
tanA =
opposite
adjacent
Ex.1 For ∆ABC, find the sine,
the cosine, and the tangent
of ∠A and ∠B.
B
10
6
C
8
A
Ex.2 Use a calculator to find the value of each expression.
Round to the nearest ten-thousandth.
a) sin 40˚
b) cos 75˚
1) Decide which
trig ratio to use
2) Write an
equation and
solve
Ex.3 Find the value of x in each triangle.
a)
b)
A
N
15
B
Angle of elevation:
angle from the
horizontal up to a
line of sight
60°
C
b
42˚
x
L
5
M
Ex.4 Suppose the angle of elevation from a rowboat ot the
top of a lighthouse is 70˚. You know that the lighthouse is 70
ft tall. How far from the lighthouse is the rowboat? Round
your answer to the nearest foot.
Angle of depression:
angle measured
below the horizontal
line of sight
Ex.5 A pilot is flying a plane 15,000 ft above the ground.
The pilot begins a 3 decent to an airport runway. How
far is the airplane from the start of the runway (in
ground distance)?
Ex.6 For ∆ABC, find the sine, cosine and tangent of ∠A.
You must determine the missing side first.
a)
b)
B
B
C
14
7
7
7
A
A
C
Ex.7 Which statement describes
the relationship between
the length of AB and the
length of BC ?
A
B
30°
60°
a) BC is
2 times as long as AB
b) BC is
3 times as long as AB
c) BC is 2 times as long as AB
d) BC is 3 times as long as AB
C
N
Ex.8 For ∆MNQ, n=10 and
the measure of ∠N is 55°.
a) Find the length m.
55°
q
M
10
m
Q
b) Find the length q.
Ex.9 A nature preserve is
building a bridge from
point C to point A.
What will be the length
of the bridge?
B
50°
59 m
C
Summary:
A
Notes #3-___
Date:______
9-1 Adding and Subtracting Polynomials (457)
W.1 Find the sin, cos, and tan of ∠A
B
6
10
A
C
W.2 Simplify each expression.
a) 2b – 6 + 9b
b) 8x2 – x2
degree
leading coefficient
-6x3 + 5x – 3
coefficients
constant term
Standard form – exponents of terms descend
Ex.1 Identify the coefficients & degree of each monomial.
a) 18
b) 3xy3
c) 6c
Class by Degree
Zero function
Constant f(x)
Linear f(x)
Quadratic f(x)
Cubic f(x)
Quartic f(x)
Quintic f(x)
nth degree poly.
Form: f(x) =
0
a (a ≠ 0)
ax + b (a ≠ 0)
ax2 + bx + c (a ≠ 0)
a3x3 + a2x2 + a1x + a0
a4x4 + a3x3 + a2x2 + a1x + a0
a5x5 + a4x4 +…+ a1x + a0
anxn + an-1xn-1 + … + a1x + a0
Class by # of terms Deg
monomial
Und
monomial
0
monomial/binomial
1
mo/bi/tri-nomial
2
mo/bi/tri/poly-nomial 3
polynomial
4
polynomial
5
polynomial
n
Ex.2 Write each polynomial in standard form and classify by
degree and number of terms.
a) -5
b) 1 x
c) -9x + 2
4
d) x2 – 6
e) -x3 + 2x + 1 f) 3x4 + 2x3 – x2 + 5x – 8
Ex.3 Find the sum. Write the answer in standard form.
a) (-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3)
Horizontally:
Vertically:
b) (6x2 – x + 3) + (-2x + x2 – 7)
Ex.4 Find the difference. Write the answer in standard form.
a) (-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1)
b) (-4x2 – 1) – (3x – 2x2)
c) (12x – 8x2 + 6) – (-8x2 – 3x + 4)
Ex.5 A small square is inside a larger
square. What is the area, in terms
of x, of the shaded region?
x
6
a) 2x – 12
b) 12 – 2x
c) 36 – 2x
d) x2 – 36
e) 36 – x2
x
6
Ex.6 Enlarge an 8” by 10” photo by a scale factor of 2x and
mount it on a mat 1.5 times as wide as the enlarged
photo and 3 inches less than 1.5 times as high.
a) Draw a diagram to represent the described
situation. Label the dimensions.
b) Write a model for the area of the mat around the
photograph as a function of x.
Summary: