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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log100 10
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 31-x= 27
U.S. soldiers fight Russian troops who have invaded New York City. Incoming missiles from Russian submarines and warships ravage the Manhattan skyline. It’s just another scenario for the
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.f(x) = 5x
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. g(x) = (3²) X
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log 10
In each exercise, evaluate the indicated logarithmic expressions without using a calculator.a. Evaluate: log2 16.b. Evaluate: log2 32 - log2 2.c. What can you conclude about log2 16, or log2 32 2 ?
In Exercises 9–20, write each equation in its equivalent logarithmic form. =8/ = 2
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. In e4 8
Fill in each blank so that the resulting statement is true.The graph of g(x) = log5(-x) is the graph of f(x) = log5 x reflected about the_______ .
a. Evaluate: log3 81.b. Evaluate: 2 log3 9.c. What can you conclude about log3 81, or log3 92?
Fill in each blank so that the resulting statement is true.The domain of g(x) = log2(5 - x) can be found by solving the inequality_________ .
a. Simplify: eln 3.b. Use your simplification from part (a) to rewrite 3x in terms of base e.
The formula A = 10e-0.003t models the population of Hungary, A, in millions, t years after 2006.a. Find Hungary’s population, in millions, for 2006, 2007, 2008, and 2009. Round to two decimal
Solve the equation x3 - 9x2 + 26x - 24 = 0 given that 4 is a zero of f(x) = x3 - 9x2 + 26x - 24.
Consider the quadratic function f(x) = -4x2 - 16x + 3.a. Determine, without graphing, whether the function has a minimum value or a maximum value.b. Find the minimum or maximum value and determine
In each exercise, evaluate the indicated logarithmic expressions without using a calculator.a. Evaluate: log2 32.b. Evaluate: log2 8 + log2 4.c. What can you conclude about log2 32, or log2(8 .
Solve each equation in Exercises 146–148. Check each proposed solution by direct substitution or with a graphing utility.ln(ln x) = 0
Solve each equation in Exercises 146–148. Check each proposed solution by direct substitution or with a graphing utility.(log x)(2 log x + 1) = 6
In Exercises 141–144, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.143. If x = 1 k In y, then y = ekx
Find the inverse of f(x) = x2 + 4, x ≥ 0.
Three of the richest comedians in the United States are Larry David (creator of Seinfeld), Matt Groening (creator of The Simpsons), and Trey Parker (co-creator of South Park). Larry David is worth
Solve each equation in Exercises 146–148. Check each proposed solution by direct substitution or with a graphing utility.(ln x)2 = ln x2
Without using a calculator, determine which is the greater number: log4 60 or log3 40.
If $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, after how long will the
Without using a calculator, find the exact value of log4[log 3(log2 8)].
In Exercises 141–144, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.If log(7x + 3) - log(2x + 5) = 4, then
In Exercises 139–142, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.logb x is the exponent to which b must
In Exercises 139–142, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The domain of f(x) = log2 x is
Graph y = g(x) by hand. (a) g(x) = 2-3x (b) g(x)= |2x - 11 (c) g(x)=(x-2)² + 2 (d) g(x)=x²-1 (e) g(x) = √-x (1) g(x)=√x (g) g(x) = x ²4+2 (h) g(x)=x²-x
Graph f(x) = -0.25x4 +0.67x3 + 9.5x2 - 20x - 50. (a) Approximate any local extrema. (b) Approximate any absolute extrema. (c) Determine where f is increasing or decreasing.
Let y vary inversely with the cube of x. If x = 1/5, then y = 150. Find y if x = -1/2.
Use the graph off to estimate any (a) Local extrema and (b) Absolute extrema. 7 2
Use the graph off to estimate any (a) Local extrema and (b) Absolute extrema. x 7
Determine whether f is a rational function and state its domain. 9 = (x)/
Write the expression as one ratio without any negative exponents. 2/3 + x1/3 x
Use the graph to express the domain and range of f. Then evaluate f(0). -3 -2 -1 2 y = f(x) 123 X
Write the expression as one ratio without any negative exponents. x1/4x-3/4 X
Find any horizontal or vertical asymptotes. f(x) = 2x²-3x + 1 2x - 1
Solve the polynomial equation. Find all complex solutions. 2x³ + 5x² + x + 12 = 0
Solve 2x3 + x2 - 6x < 0.
Use the graph off to estimate each of the following. (a) Where f is increasing or decreasing (b) The zeros of f (c) The coordinates of any turning points (d) Any local extrema 32 y = f(x)
Solve the equation and inequalities. (a) f(x)=0 (b) f(x) >0 (c) f(x) < 0 y = f(x) 2
Solve the equation and inequalities. (a) f(x)=0 (b) f(x) >0 (c) f(x) < 0 y = f(x) T -'' X
Solve the equation and inequalities. (a) f(x)=0 (b) f(x) >0 (c) f(x) < 0 y = f(x) X
Use the factor theorem to decide if x - k is a factor of f(x) for the given k. f(x) = x³ = 6x² + 11x - 6 k = 2
Solve the polynomial equation. Find all complex solutions. ジャー
Find any horizontal or vertical asymptotes. f(x) = x² + 2x + 1 2x²-3x - 5
Solve the polynomial equation. Find all complex solutions. zX6 + x = 6 + 5*
Complete the following. (a) State the degree and leading coefficient of f. (b) State the end behavior of the graph of f. f(x) = 2 - x
Solve the polynomial equation. Find all complex solutions. x² + x³ = 16 - 8x 16 - 8x - 6x²
Complete the following. (a) Identify where f(x) is undefined or f(x) = 0. (b) Solve f(x) > 0. (c) Solve f(x) < 0. -3-2-1 y = f(x) I 23
Divide each expression. (a) 4a³-8a² + 12 4a² (b) 2x³ - 4x + 1 x-1
Find any horizontal or vertical asymptotes. f(x) = 6x²-x-2 2x²+x-6
Use the graph of f(x) = 2x4 - x2 - 1 to predict the number of real zeros and the number of nonreal complex zeros of f. Find these zeros symbolically. 7 -2 2 = 2x²-x²-1
Find any horizontal or vertical asymptotes. f(x) = 3x(x + 2) (x + 2)(x - 1)
Solve the polynomial equation. Find all complex solutions. x² + 2x² = x³ X
Use transformations of the graphs of y = √x, y = 3√x, or y = 4√x to graph y = f(x). x-A = (x)/
Solve the polynomial equation. Find all complex solutions. 3x³+4x²+ 6 = x
Write a polynomial f(x) in complete factored form that has degree 3, leading coefficient 4, and zeros 1, 3i, and -31. Then write f(x) in expanded form.
Complete the following. (a) Identify where f(x) is undefined or f(x) = 0. (b) Solve f(x) > 0. (c) Solve f(x) < 0. y = f(x) 12
Complete the following. (a) Identify where f(x) is undefined or f(x) = 0. (b) Solve f(x) > 0. (c) Solve f(x) < 0. 3 2 y = f(x) 23
Use transformations of the graphs of y = √x, y = 3√x, or y = 4√x to graph y = f(x). f(x)=√x+1-2
Find any horizontal or vertical asymptotes. f(x) = = X 1³- X
If a zero of f is i, find the complete factored form of f(x) = x4 + x3 + 2x2 + x + 1.
Find any horizontal or vertical asymptotes in the graph of f(x) 2x² + x - 15 3x² + 8x - 3
Find any horizontal or vertical asymptotes. f(x) = 1²-9 x + 3
Sketch a graph of a quartic (degree 4) function with a negative leading coefficient, three x-intercepts, and three turning points.
Find the difference quotient of f. X * = (x)/
State the domain of f(x) = 3x - 2/5x/4. Identify any hori- 5x zontal or vertical asymptotes in the graph of f.
State the end behavior of f(x) = 4 + 3x - x3.
Find the difference quotient of f. f(x)=√x
Solve.(a) (3x - 1)/ (1 - x )= 1(b) 3 + 8/x = 35/x2(c) (1/x - 1) - (1/3(x + 2) = 1/(x2 + x - 2)
Let S = {(-3, 4), (-1, -2), (0,4), (1, -2).(-1,5)}. (a) Find the domain and range of S. (b) Is S a function?
State the degree and leading coefficient of the polynomial f(x) = 4 + x = 2x2 - 7x3.
Find the exact distance between (-1, 4) and (3, -9).
Complete the following. (a) State the degree and leading coefficient of f. (b) State the end behavior of the graph of f. f(x) = 4x
Use the given graph of y = f(x) to sketch a graph of each equation. (a) y = f(x + 2) - 1 (c) y = f(-x) + 1 32 (b) y = -2f(x) (d) y = f(x) y = f(x) 23
Use division to express the (Dividend) as (Divisor)(Quotient) + (Remainder). 2x³ + x² - 2x 2x + 1
Find any horizontal or vertical asymptotes. f(x) = x+1 x² + 3x - 10
Write the complete factored form of the polynomial f(x), given that k is a zero. f(x) = 2x4x³ - 13x² - 6x k=-2
Solve the polynomial equation. Find all complex solutions. x + 5 = 0
Determine any (a) Local extrema and (b) Absolute extrema. 1 + zx = (x) 8
Solve the equation and inequalities. (a) f(x)=0 (b) f(x) >0 (c) f(x) < 0 2 y = f(x)
Find all complex solutions. x³ + x = 0
Write the complete factored form of the polynomial f(x), given that k is a zero. f(x) = 35x4 + 48x³ - 41x² + 6x k = ²/
Solve the polynomial equation. Find all complex solutions. x²2x³ + x²-2x = 0
Determine any (a) Local extrema and (b) Absolute extrema. zx − 1 = (x) 8 -
Find any horizontal or vertical asymptotes. f(x) = 4x³ - 2 x+2
Use division to express the (Dividend) as (Divisor)(Quotient) + (Remainder). 1-x {* + zx = 1 x
Use transformations of graphs to sketch a graph of y = 2√x + 1.
Find all complex solutions. x² + 3x² + 2 = 0
The graph of a nonlinear function f is shown. Solve each equation or inequality. (a) f(x) = 0 (b) f(x) > 0(c) f(x) ≤ 0 32 y = f(x) X
Write the complete factored form of the polynomial f(x), given that k is a zero. f(x) = -4x³x² + 51x - 36 k = -4
Find all real solutions. Check your results. 1 1 2x + 12x - 1 2 4x² - 1
Find any horizontal or vertical asymptotes. f(x) 3 x²-5
Solve the equation and inequalities. (a) f(x)=0 (b) f(x) >0 (c) f(x) < 0 y = f(x)
Determine any (a) Local extrema and (b) Absolute extrema. g(x) = 1 - 3x
Solve the polynomial equation. Find all complex solutions. x³ = 2x² - 7x + 14
Write the complete factored form of the polynomial f(x), given that k is a zero. f(x) = 3x³ - 11x² - 35x + 75 k=5

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