Chapter 6 Homework required for retake

6-8. Make a table like the one below. Choose points in each of the locations listed at
the top of the table and write in the coordinates of the points you have chosen.
a. What do you notice about the coordinates of the points on the x-axis?
b. Make a conjecture about the coordinates of points that lie on any of the
coordinate axes.

6-11. Solve each exponential equation for x.
a. 10x = 16
b. 10x = 41
c. 3x = 729
d. 10x = 101

6-13. Multiply or divide and simplify each of the following expressions.
a.
b.

6-21. For each of the following equations, find every point where its threedimensional graph intersects one of the coordinate axes. That is, find the x-, y- and zintercepts. Express your answer in (x, y, z) form.
a. 6y + 15z = 60
b. 3x + 4y + 2z = 24
c. (x + 3)2 + z2 = 25
d. z = 6

6-27. Sketch the graph of y = log5 (x − 2) and describe how the graph is transformed
from the parent graph.

6-35. On isometric dot paper, graph the system of equations below. What shape is the
intersection? Use color to show the intersection clearly on your graph. (GET
ISOMETRIC DOT PAPER FROM ME!)
10x + 6y + 5z = 30
6x + 15y + 5z = 30

6-39. Simplify each of the following expressions.
a.
b.

6-51. Use the algebraic strategies you developed in today's lesson to solve the system
of equations below. Be sure to check your solution.
2x + y − 3z = −12
5x − y + z = 11
x + 3y − 2z = −13

6-71. Solve the system of equations below and then check your solution in each
equation. Be sure to keep your work well organized.
x − 2y + 3z = 8
2x + y + z = 6
x + y + 2z = 12

6-73. This problem is a checkpoint for multiplying and dividing rational expressions.
It will be referred to as Checkpoint 6A.
Multiply or divide each pair of rational expressions. Simplify the result.
a.
b.

6-80. Solve the system of equations below and then check your solution in each
equation. Be sure to keep your work well organized.
x + 2y − z = −1
2x − y + 3z = 13
x + y + 2z = 14

6-81. Find an equation for the parabola that passes through the points (−1, 10), (0, 5),
and (2, 7).

6-83. Add or subtract and simplify each of the following expressions. Justify that each
step of your process makes sense.
a.
b.

6-86. Shift the graph of log x up 3 units and to the right 6. Graph both the original and
the transformed graph on the same set of axes and write the equation for the
transformed graph.

6-87. Given f(x) = 2x2 − 4 and g(x) = 5x + 3, find the value of each expression below.
a. f(a)
b. f(3a)
c. f(a + b)
d. f(x + 7)
e. f(5x + 3)
f. g(f(x))

6-103. Solve each system of equations below.
a. −4x = z − 2y + 12
y + z = 12 − x
8x − 3y + 4z = 1
b. 3x + y − 2z = 6
x + 2y + z = 7
6x + 2y − 4z = 12
c. What does the solution in part (b) tell you about the graphs?

6-113. Solve each of the following equations to the nearest 0.001.
a. (5.825)(x−3) = 120
b. 18(1.2)(2x−1) = 900

6-116. Sketch the graph of y = log3(x + 4) and describe the transformation from its
parent graph.

6-121. Add or subtract and simplify each of the following expressions. Justify that
each step of your process makes sense.
a.
b.

6-128. Give an example of an equation that requires the use of logarithms to solve it.

6-131. Find the equation of the parabola that passes through the points (–2, 24), (3, –
1), and (–1, 15).

6-132. Use
to complete parts (a) through (e) below.
a. What are the domain and range of f(x)?
b. What is the inverse of f(x)? Call it g(x).
c. What are the domain and range of g(x)?
d. Find an expression for f(g(x)).
e. Find an expression for g(f(x)). What do you notice? Why does this happen?

6-135. Add or subtract each expression below. Be sure to simplify.
a.
b.
c.
d.
6-139. Solve for x without using a calculator.
a.
x = log25(5)
b. logx(1) = 0
c. 23 = log10(x)

6-141. If f(x) = x4 and g(x) = 3(x + 2), find the value of each expression below.
a. f(2)
b. g(2)
c. f(g(2))
d. g(f(2))
e. Are f(x) and g(x) inverses of each other? Justify your answer.

6-145. This problem is a checkpoint for adding and subtracting rational expressions. It
will be referred to as Checkpoint 6B.
Add or subtract each pair of rational expressions. Simplify the result.
a.
b.

CL 6-148. Graph in three dimensions. GET GRAPH PAPER FROM ME!
a. (2, 3, 1)
b. (−2, 3, 0)
c. 2x + y −z = 6

CL 6-149. Determine the point of intersection of the three planes.
x+y+z=3
2x − y + 2z = 6
3x + 2y − z = 13
. x + y + 4x = 5
−2x + 2z = 3
3x + y −2z = 0

CL 6-150. The parabola y = ax2 + bx + c passes through the points (2, 3), (−1, 6), and
(0, 3). Determine:
. The equation of the parabola.
a. The vertex of the parabola.
b. The x-intercepts of the parabola.

CL 6-151. Solve each equation to the nearest thousandth (0.001).
. 2x = 17
a. 5x3 = 75
b. 5(3x+1) = 85
c. log3(x + 1) = −2

CL 6-154. Use your Parent Graph Toolkit or make a table to graph y = log2(x).

CL 6-155. Use your answer to the previous problem to graph y = 1 + log2(x − 3).
State the equation of the new asymptote and the new x-intercept.

CL 6-158. Consider the function
a. What are the domain and range of f(x)?
b. If g(x) = x − 10, what is f(g(x))?
c. What are the domain and range of f(g(x))?
d. Is f(g(x)) = g(f(x)) Justify why or why not.