math algebra
SECTION 3.1
Algebraic
For the following exercise, determine whether the relationship represents y as a function of x. If the relationship represents a function then write the relationship as a function of x using f as the function.
1. x+y2=5
0. Consider the relationship 7n-5m=4.
a. Write the relationship as a function n = k(m).
a. Evaluate k(5).
a. Solve for k(m) = 7.
Graphical
0. Given the following graph
a. Evaluate f(4)
a. Solve for f(x) = 4
For the following exercise, use the function f represented in table below. (4 points)
|
x |
-18 |
-12 |
-6 |
0 |
6 |
12 |
18 |
|
f(x) |
24 |
17 |
10 |
3 |
-4 |
-11 |
-18 |
0. Answer the following:
a. Evaluate f(-6).
a. Solve f(x) = -11
a. Evaluate f(12)
a. Solve f(x) = -18
SECTION 3.2
Algebraic
For the following exercise, find the domain and range of each function and state it using interval notation.
0. f(x)=9-2x5x+13
Numeric
For the following exercise, given each function f, evaluate f (3), f (-2), f (1), and f (0). (4 points)
0.
SECTION 3.3
Algebraic
For the following exercise, find the average rate of change of each function on the interval specified in simplest form.
0. k(x)=23x+1on [2, 2+h]
For the following exercise, find the average rate of change of each function on the interval specified.
0. g(x)=3x2-23x3 on [1, 3]
Real-World Applications
0. Near the surface of the moon, the distance that an object falls is a function of time. It is given by d(t)=1.6t2, where t is in seconds and d(t) is in meters. If an object is dropped from a certain height, find the average velocity of the object from t = 2 to t = 5.
SECTION 3.4
Algebraic
For the following exercise, determine the domain for each function in interval notation. (4 points)
0. f(x)=2x+5 and g(x)=4x+9, find f-g, f+g, fg, and fg
For the following exercise, use each set of functions to findg(f(h(x))). Simplify your answers. (4 points)
0. f(x)=x3-3,g(x)=6-x, and h(x)=2x
Numeric
For the following exercise, use the function values for f and g shown in table below to evaluate each expression.
|
x |
-8 |
-6 |
-4 |
-2 |
0 |
2 |
4 |
6 |
8 |
|
f(x) |
15 |
8 |
9 |
6 |
3 |
0 |
-3 |
-6 |
-8 |
|
g(x) |
-6 |
-1 |
3 |
7 |
11 |
15 |
-8 |
23 |
0 |
0.
a. fg(4)
b. fg(-8)
c. gf(-6)
d. gf(8)
For the following exercise, use each pair of functions to findf(g(-1))andg(f(-1)).
0. f(x)= -62x+5, g(x)= -x2+7
Real-World Applications
0. The radius r, in inches, of a spherical balloon is related to the volume, V, by the following:
r=33V4
Air is pumped into the balloon, so the volume after t seconds is given byV(t)=15+18t. Find the composite function r(V(t)) and use it to answer the following questions. Round the results to the nearest hundredth of a second.
a. At what exact time is the radius 10 inches?
a. At what exact time is the radius 20 inches?
a. At what exact time is the radius 30 inches?
For the following exercise, determine the interval(s) on which the function is increasing and decreasing.
0. h(x)=6(x-8)2+7
Numeric
For the following exercise, determine whether the function is odd, even, or neither.
0. f(x)=(x+4)2
For the following exercise, write a formula for the function f that results when the graph of a given toolkit function is transformed as described.
0. The graph of f(x)=x is reflected over the x-axis, shifted vertically up 1 unit, horizontally compressed by a factor of 37.
SECTION 3.6
Algebraic
0. Describe the situation in which the distance that point x is from 18 is at least 13 units. Express this using absolute value notation.
For the following exercise, find the x- and y-intercepts of the graph of the function.
f(x)=x+9-11
For the following exercise, find a domain on which the function f is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of f restricted to that domain.
0. f(x)=x+112-14
Graphical
For the following exercises, use a graphing utility to determine whether each function is one-to-one.
0. f(x)=x-32+6
Numeric
For the following exercise, evaluate or solve, assuming that the function f is one-to-one.
0. If f(23)=32, find f-132.
Real-World Applications
0. The area A of a circle is a function of its radius given by A(r)=r2. Express the radius of a circle as a function of its area. Call this function r(A). Find r(64)and interpret its meaning.
SECTION 4.1
Algebraic
For the following exercise, determine whether the equation of the curve can be written as a linear function.
0. x+6=4y-2
For the following exercise, determine whether the lines given by the equations below are parallel, perpendicular, or neither.
37. 3x+8y=12 and 15-8y=3x
For the following exercise, use the description of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?
0. Line 1: Passes through (2, 3) and (4, −1)
Line 2: Passes through (6, 3) and (12, 6)
For the following exercise, write an equation for the line described.
0. Write an equation for a line perpendicular to p(t)= -11t+14 and passing through the point (−3, −1).
Graphical
For the following exercise, find the slope of the lines graphed.
For the following exercise, sketch a line with the given features.
0. A y-intercept of (0, -7) and slope of 35
For the following exercise, sketch the graph of the equation.
g(x)=2x3-12