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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
Sketch a graph of y = f(x). f(x) = 3(2-x)
Combine the expressions by writing them as a logarithm of a single expression. log4 - logx + 7log Vx
Combine the expressions by writing them as a logarithm of a single expression. In 3e In- 4e
Find f-1(x). f(x) = x-1 2
Sketch a graph of y = f(x). f(x) = 3*
Combine the expressions by writing them as a logarithm of a single expression. 2log(x² − 1) + 4log(x - 2) - logy -
For the given g(x), evaluate each of the following. (a) g(-3) (b) g(b) (c) g(x3) (d) g(2x - 3) g(x) = 4x x+3
Find f-1(x). £³7 − 1 = (x)ƒ
Find f-1(x). f(x) = 2x³-5
Sketch a graph of y = f(x). f(x) = 1.5*
Combine the expressions by writing them as a logarithm of a single expression. log3x + log3√x + 3 − log(x-4) -
Find f-1(x). 0 = x ¹1 x = (x)/ 'I
Sketch a graph of y = f(x). f(x) = ½ (3¹) 3
Sketch a graph of y = f(x). f(x) = 1/2 (2³)
Sketch a graph of f. f(x) = log₂x
Sketch a graph of f. f(x) = log₂.x²
For the given g(x), evaluate each of the following. (a) g(-3) (b) g(b) (c) g(x3) (d) g(2x - 3) g(x) = x + 3 2
Find f-1(x). f(x) = -| 1 2x
Find f-1(x). f(x) = (x + 2)², x = -2
Sketch a graph of y = f(x). f(x) = 4(2-¹)
Sketch a graph of f. f(x) = log3|x|
Find f-1(x). f(x) = all 2 Vx
Sketch a graph of f. f(x) = log42x
Sketch a graph of y = f(x). f(x) = 9(3-³)
Use the given f(x) and g(x) to evaluate each expression. f(x) = √x + 5, g(x) = x² (a) (fᵒg)(2) (b) (gof)(-1)
Find f-1(x). f(x) = 6 - 3(2x-4)
Sketch a graph of y = f(x). f(x) = 2(1)*
If possible, simplify f(x). Find the domain of f. f(x) = logg V23x
Use the given f(x) and g(x) to evaluate each expression. f(x)=x²-41, g(x) = 2x² + x + 1 (a) (fog)(1) (b) (gof)(-3)
Sketch a graph of y = f(x). f(x) = 5(!)*
If possible, simplify f(x). Find the domain of f. f(x) = log V104x
Use the given f(x) and g(x) to evaluate each expression. f(x) = 5x - 2₁ g(x) = |x| 2, (a) (fog)(-4) (b) (gof)(5)
Sketch a graph of y = f(x). f(x) = 2(1)*
If possible, simplify f(x). Find the domain of f. f(x) = ln(1-2¹)
Use the given f(x) and g(x) to evaluate each expression. {(x) = x - 4² (a) (fog)(3) g(x) = 5 (b) (gof)(8)
Find f-1(x). f(x) = 3x x-1
If possible, simplify f(x). Find the domain of f. f(x) = ln(1-x)
Sketch a graph of y = f(x). f(x) = 2(3¹)
Find f-1(x). f(x) = 3x x-1
The table shows the density y of a species of insect measured in thousands per acre after x days.(a) Find a function f that models the data. (b) Use f to estimate the density after a long time. x 2 y 0.38 8 10 12 14 1.24 2.86 4.22 4.78 4.94 4.98 46
Expand the expression. If possible, write your answer without exponents. X ²√3 V In
Use the graph of y = f(x) to determine if f is one-to-one. Does f have an inverse? y = f(x) 3
Find the domain of f and write it in set- builder or interval notation. f(x) = log(4- V2-x)
Use f(x) and g(x) to find a formula for each expression. Identify its domain. (a) (f + g)(x) (c) (fg)(x) (b) (f- g)(x) (d) (f/g)(x)
Use f(x) and g(x) to find a formula for each expression. Identify its domain. (a) (f + g)(x) (c) (fg)(x) (b) (f- g)(x) (d) (f/g)(x)
Use f(x) and g(x) to find a formula for each expression. Identify its domain. (a) (f + g)(x) (c) (fg)(x) (b) (f- g)(x) (d) (f/g)(x)
The table lists the atmospheric density y in kilograms per cubic meter (kg/m3) at an altitude of x meters.(a) Find a function f that models the data.(b) Predict the density at 7000 meters. (The actual value is 0.59 kg/m3.) x (m) y (kg/m³) x (m) y (kg/m³) 0 1.2250 20,000 0.0889 5000 10,000
Find the domain of f and write it in set- builder or interval notation f(x) = logs (5 - 25)
Use f(x) and g(x) to find a formula for each expression. Identify its domain. (a) (f + g)(x) (c) (fg)(x) (b) (f- g)(x) (d) (f/g)(x)
Use the graph of y = f(x) to determine if f is one-to-one. Does f have an inverse? 2 + y = f(x) VAA xx
As age increases, so does the likelihood of coronary heart disease (CHD). The percentage P of people x years old with signs of CHD is shown in the table.(a) Evaluate P(25) and interpret the answer. (b) Find a function that models the data. (c) Graph P and the data. (d) At what age does a person
Expand the expression. If possible, write your answer without exponents. logs 25x³
Use f(x) and g(x) to find a formula for each expression. Identify its domain. (a) (f + g)(x) (c) (fg)(x) (b) (f- g)(x) (d) (f/g)(x)
Use the graph of y = f(x) to determine if f is one-to-one. Does f have an inverse? -3 3 y = f(x) 3
Find the domain of f and write it in set- builder or interval notation. f(x) = ln (√3x - 1)
Use f(x) and g(x) to find a formula for each expression. Identify its domain. (a) (f + g)(x) (c) (fg)(x) (b) (f- g)(x) (d) (f/g)(x)
Expand the expression. If possible, write your answer without exponents. log₂ 32
The following table shows the number of cell phone subscriptions in India in billions for selected years.(a) Find a function C(x) that models the data, where x is years after 2005. (b) Predict the number of cell phone subscriptions in 2014. Year 2005 2006 2007 2008 0.21 0.40 Cell Phones 0.05
Expand the expression. If possible, write your answer without exponents. In- A
The height H of a tree in feet after x years is listed in the table.(a) Evaluate H(5) and interpret the answer. (b) Find a function that models the data. (c) Graph H and the data. (d) What is the tree's age when its height is 25 feet? (e) Did your answer involve interpolation or extrapolation?
The numbers N of radio stations on the air for selected years x are listed in the table.(a) Find a function that models the data. (b) Graph N and the data. (c) Predict when the number of radio stations on the air might reach 16,000. X 1970 1980 1990 2000 2010 8566 10,788 12,808 14,420 N(x) 6760
Expand the expression. If possible, write your answer without exponents. log, (0.25(x + 2)³)
Heavier birds tend to have larger wings than smaller birds. For one species of bird, the table lists the area A of the bird's wing in square inches if the bird weighs w pounds.(a) Find a function that models the data. (b) Graph A and the data. (c) What weight corresponds to a wing area of 500
Use f(x) and g(x) to find a formula for each expression. Identify its domain. (a) (f + g)(x) (c) (fg)(x) (b) (f- g)(x) (d) (f/g)(x)
Expand the expression. If possible, write your answer without exponents. (-(9- D)100'0) So
Use f(x) and g(x) to find a formula for each expression. Identify its domain. (a) (f + g)(x) (c) (fg)(x) (b) (f- g)(x) (d) (f/g)(x)
The table is a complete representation of f. Use the table to determine if f is one-to-one and has an inverse. 0 2 0 x-2 f(x) 4 2 4 -2
The table is a complete representation of f. Use the table to determine if f is one-to-one and has an inverse. X 0 2 4 0 4 f(x) -1 6 1 8
Heavier birds tend to have a longer wing span than smaller birds. For one species of bird, the table lists the length L of the bird's wing span in feet if the bird weighs w pounds.(a) Find a function that models the data. (b) Graph L and the data. (c) What weight corresponds to a wing span of 2
The table is a complete representation of f. Use the table to determine if f is one-to-one and has an inverse. x-2 -1 0 f(x)| 4 1 0 品 1 2 l 4
Expand the expression. If possible, write your answer without exponents. logs (x-4)4
Which function becomes larger for 0 ≤ x ≤ 10: f(x) = 2x or g(x) = x2?
Expand the expression. If possible, write your answer without exponents. (3x - 2)² x² +1 logs
Expand the expression. If possible, write your answer without exponents. log₂ L VX
Which function becomes smaller for 4 ≤ x ≤ 12: f(x) = = or g(x) = 台
If you were offered l₵ for the first week of work, 3₵ for the second week, 5₵ for the third week, 7₵ for the fourth week, and so on for a year, would you accept the offer? Would you accept an offer that pays l₵ for the first week of work, 2 for the second week, 4 for the third week, 8₵
Which function becomes larger for 0 ≤ x ≤ 10: f(x) = 4 + 3x or g(x) = 4(3)x?
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = 2x - 7
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. 1-₂x = (x)f
Which function becomes larger for 0 ≤ x ≤ 10: f(x) = 2x + 1 or g(x) = 2-x?
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = -2x² + x
Near New Guinea there is a rela- tionship between the number of bird species found on an island and the size of the island. The table lists the number of species of birds y found on an island with an area of x square kilometers.(a) Find a function f that models the data. (b) Predict the number of
Use f(x) and g(x) to find a formula for each expression. Identify its domain. (a) (f + g)(x) (c) (fg)(x) (b) (f- g)(x) (d) (f/g)(x)
Expand the expression. If possible, write your answer without exponents. log. Ax
State the end behavior of f. f(x) = -2x³ + 4x - 2
Find the average rate of change of f(x) = x3 - x from x = -3 to x = -2.
Complete the following. (a) State the degree and leading coefficient of f. (b) State the end behavior of the graph of f. f(x) = -4 + 5x
The polynomial given by f(x) = 1/2x3 - 3x2 + 11/2x - 3 has zeros 1, 2, and 3. Write its complete factored form.
Determine the type of symmetry that the graph of g(x) = x5 - 4x3 exhibits.
Simplify the expression without a calculator. 41/641/3
Solve the polynomial inequality. (a) Symbolically and (b) Graphically. Use interval notation to write the solution set. x³-x>0
Write the expression as one ratio without any negative exponents. +1)x-1/3-2/3 (x + 1)²
Solve the polynomial inequality. (a) Symbolically and (b) Graphically. Use interval notation to write the solution set. XT ==x + cx
Use least-squares regression to find a polynomial that models the data in Exercise 4.Data from Exercise 4:Plot the data in the table. -3.2 y -11 ५ -2 15 0 -10 2 15 3.2 -11
Determine if f is even. odd, or neither. f(x) = 2x6 2x6 - 5x²-x²
The boundedness theorem shows how the bottom row of a synthetic division is used to place upper and lower bounds on possible real zeros of a polynomial function. Let P(x) define a polynomial function of degree n ≥ 1 with real coefficients and with a positive leading coefficient. If P(x) is
Solve the polynomial inequality. (a) Symbolically and (b) Graphically. Use interval notation to write the solution set. 8x³ < 27
Solve the equation √5x4 = x - 2.
Simplify each expression without a calculator. (a) -43/2 (b) (8-2)1/3 (c) 3√272
Solve the polynomial inequality. (a) Symbolically and (b) Graphically. Use interval notation to write the solution set. x4 13x² + 36
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