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HONORS REVIEW PACKET SEMESTER 1 : Advanced Algebra w/ Trig
CHAPTER 1 – Linear and Quadratic Equations
Solve for x.
1.) x
2
x
6
5
4=− 2.) ( ) 20x25x2x8 −=+−−
3.) 23x
2
12x
5
−
=
+
4.) 2x
3
4x
4
4x
x2
22+
+
−
=
−
5.) 2x2 + 5x + 3 = 0 6.) 49x42=
7.) 4x2 + 9 = 12x 8.) (2x + 3)2 = 9
9.) 2x2 – 2x + 5 = 0 10.) 8x4x2
=+
11.) 010xx32
=−+ 12.) 207x67x1022−=−
Perform the indicated operation.
13.) ( ) ( )i28i54 +−−+ 14.) (5 + 3i)(2 – i) 15.) ( )2i23 +
Solve each equation or inequality. For the inequalities, give answer in interval notation.
16.) 1053x =− 17.) 33x23
−=+
18.) 8xx42x23+=+ 19.) 2x – 5 < 3(x – 2)
20.) 123x5 <−≤− 21.) 4
3
3
1x
2
1<
+≤
22.) 534 <++x 23.) 243x ≥+
24.) 9785x =+−
25.) A bank loaned out $12,000, part of it at the rate of 8% per year and the rest at the rate of 18% per year. If the interest received totaled $1,000, how much of it was loaned at 8%? CALC. 26.) A coffee manufacturer wants to market a new blend of coffee that sells for $3.90 per pound by mixing two coffees that sell for $2.75 and $5 per pound respectively. What amounts of each coffee should be blended to obtain 100 lbs of the desired mixture? CALC. (round to whole number) 27.) A townhouse that was bought for $275,000. The value has increased in value by 8%. What is the value of the townhouse? CALC. 28.) An electrician charges $50 for a house visit and $75 an hour for the work that he completes. What is the total charge if the electrician works for 6.5 hours? CALC.
CHAPTER 3 – Functions
1.) Find the domain of each function.
a.) f(x) = x2 + 14x + 40 b.) f(x) = 16
23
2−
−
x
x
c.) f(x) = 3x +
2. Find the following for the functions f(x) = 2 – x and g(x) = 3x2 + 5
a.) g(-3) b.) f(-x) c.) (f + g) (5)
d.) (g – f)(-3) e.) (f ⋅g)(x) f.) -f(x)
g.) Find the average rate of change of g from -1 to 3.
3.) Determine (algebraically) whether the function f(x) = x3 – x – 2 is even, odd, or neither.
4.) The graph of f(x) = x is shifted to the right 4 units, stretched vertically by a factor of 3, reflected
over the x-axis and shifted up 5 units. Write the equation of the new function g(x).
5.) Graph using transformations for g(x) = (x + 1)3 – 3.
6. Use the graph of y = f(x) to the right to answer the following questions.
a.) Find the domain of f.
b.) Find the range of f.
c.) Determine f(-2).
d.) Solve for f(x) = 4.
e.) List the x-intercepts, if any exist.
f.) List the y-intercepts, if any exist.
g.) Find the zeros of f.
h.) Solve f(x) > 0.
i.) List the intervals where f is decreasing.
j.) List the intervals where f is increasing.
k.) List any local maximum value(s) and the x at which it occurs.
l.) List any local minimum value(s) and the x at which it occurs.
m.) List any absolute maximum value(s) and the x at which it occurs.
n.) List any absolute minimum value(s) and the x at which it occurs.
7.) Graph the function f(x) =
≥−
<+−
3x,5x3
2
3x,4x
8) The graph of a piecewise defined function is given. State the piecewise function.
CHAPTER 4 – Linear and Quadratic Functions
1.) Find the vertex and axis of symmetry of the quadratic function.
f(x) = x2 – 6x + 1
2.) Find the vertex and intervals where the function is increasing and decreasing.
86xxf(x)2
−+−= 3 .
3.) Determine whether the given function has maximum or minimum value. Also state the value.
48xxf(x)2
−+−=
4.) Find the quadratic function in vertex form with a vertex of (-1,2) and containing the point (3,6).
5.) Write the equation of this quadratic function in vertex form.
6.) Graph the quadratic function ( ) 9++−=2
2xf(x) using transformations. Plot 5 points.
Vertex: __________ Axis of Symmetry: __________
Domain: __________ Range: __________
7.) Graph the quadratic function f(x) = x2 – 2x – 3 using the vertex and intercepts. Plot 5 points.
vertex: ___________ y-intercept: _____________
x-intercept(s): _____________
8.) Solve each quadratic inequality. Put answer in interval notation.
a.) 10x2x2
+< b.) 0166xx2
≥−+
9.) CALC. A projectile is thrown upward so the height H in feet after t seconds is represented by the
function t100t16)t(H2+−= . In how many seconds will the object be at the maximum height?
10.) CALC. The height h in feet of an object after t seconds is represented by 10t24t16)t(h2
++−= .
Find the maximum height of the object.
11.) An engineer collects data showing the speed x of a given car model & its average miles per gallon M.
CALC. Determine whether a linear or quadratic model best fits the data.
a.) Make a scatter diagram on your calculator.
b.) Find this model. (Round to 4 decimal places)
Speed, x Miles per gallon
M
20 18
30 20
40 23
50 25
60 26
70 24
80 22
CHAPTER 5 – Polynomial and Rational Functions
Write a polynomial function of degree 3 in standard form with the given zeros.
1. Zeros: 1 (mult. 2), 4 2. Zeros: 5, 2i
Graph the polynomial function.
3. 2
3)1)(x(xf(x) −+= 4 4. 2
2)3)(x(xf(x) −+−= x
Real Zeros: Real Zeros:
Cross / Touch x-axis: Cross/Touch x-axis:
Y-Int: Y-Int:
End Behaviors: End Behaviors:
5. Graph the rational function 10x3x
4)x(R
2−−
=
VA: HA:
X-Int: Y-Int:
Domain: Range:
Find the domain and the horizontal asymptote of each rational function.
6. 7x3
5x2)x(R
2
+
−= 7.
145xx
2xG(x)
2
2
−+
=
Domain: Domain:
HA: HA:
8. Find the x-intercepts and y-intercept of the graph of the function 187xx
109xxf(x)
2
2
−+
−−= .
9. Find the vertical and horizontal asymptotes of the functions
a.) 2410xx
5xR(x)
2
2
−+
−= b.)
9x
2xR(x)
2−
+= .
10. Find all the zeros of the function 1816x7xxf(x)23
+−+= given that one zero is 9− .
11. Find all the zeros of the function 1223x3x2xf(x)23
+−−= given that one zero is 3− .
12. CALC. Find all the zeros of the function 6x10x7x)x(f23
−++= .
13. CALC. Find all zeros and linear factors of the function 53xx3x2xf(x)234
−+−+= 3 .
CHAPTER 6 – Exponential and Logarithmic Functions
1. For the functions f(x) = 3x – 5 and g(x) = 1 – 2x2, find the following:
a.) g(f(-2)) b.) f(g(2)) c.) f(g(x)) d.) g(f(x))
2. Is the function {(-1,2), (-3,4), (4,2), (5, -3)} one-to-one? Explain your answer.
3. Find the inverse of each one-to-one function.
a.) f(x) = 3x – 5 b.) g(x) = x3
x2
+
−
4. Change into a log expression. a) 1512x
= b) 19eM =
5. Change into an exponential expression. a) x375log4
= b) 34log9n
=
6. Write as a single log. ylogylog3xlog2 +−
7. Write as the sum and/or difference of logs.
34
y
xlog
8. Solve. a) x2
3x
82
1=
+
b) 4xlog3
= c) ( ) 1x3xlog 2
10=− d) 16025
3x=⋅
−
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