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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

Fill in each blank so that the resulting statement is true.The change-of-base property for logarithms allows us to write logarithms with base b in terms of a new base a. Introducing base a, the
Fill in each blank so that the resulting statement is true.For each of the scatter plots in Exercises 4–6, determine whether an exponential function, a logarithmic function, or a linear function is
Fill in each blank so that the resulting statement is true.logb 1 =_______
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places.5√3
Expand the expression. If possible, write your answer without exponents. logs √x + y² √ 2 + 1
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x)
Find C and a so that f(x) = Cax satisfies the given conditions. f(-1) = and f(1) = 4
Combine the expressions by writing them as a logarithm of a single expression. In √5 - In 25 V5
Sketch a graph of y = f(x). Identify the domain of f. f(x) = log(-x)
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = 3x - x³
Find C and a so that f(x) = Cax satisfies the given conditions. f(-2) = and f(2)= 18
Solve the polynomial inequality. Use interval notation to write the solution set. x³ > 0 V
Use the tables to evaluate, if possible. 1 3 39 x-10 f(x) 35 7 9 (a) (f + g)(1) (c)(fg)(-1) x-10 g(x) -2 0 (b) (f - g)(3) (d) (f/g)(0) 3 9
The graph shows the amount of water in a swimming pool x hours past noon. Find the slope of each line segment and interpret each slope. Water (gallons X 1000) 1 D 2 3 4 5 Time (hours)
Give the domain of the power function. Approximate f(3) to the nearest hundredth. x¹/3 = 4
Give the domain of the power function. Approximate f(3) to the nearest hundredth. x² = 1024
Between 1950 and 1980 the use of chemical fertilizers increased. The table lists worldwide average usage y in kilograms per hectare of cropland x years after 1950. (a) Graph the data. Are the data
Give the domain of the power function. Approximate f(3) to the nearest hundredth. √x - 2 = x - 4
There is a procedure to determine whether data can be modeled by y = axb, where a and b are constants. Start by taking the natural logarithm of each side of this equation.If we let z = Iny, d = Ina,
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)
Find a function that models the data. Choose from exponential, logarithmic, or logistic functions. 2 y 0.72 0.72 3 0.86 4 1.04 5 6 1.24 1.24 1.49 7 1.79
Expand the expression. If possible, write your answer without exponents. In 2x + 6 (x + 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)
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)
If major reform had occurred in the Social Security system, individuals would have invested some of their contributions into individual accounts. These accounts would be managed by financial firms,
Find f-1(x) if Identify the domain and range of f and of f-1. f(x) = √x+1, x2 -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. +4 Vx-1 log.
Expand the expression. If possible, write your answer without exponents. log₂ I-*A √1+x²
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)
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = |2x - 5|
Find C and a so that f(x) = Cax satisfies the given conditions. f(0) = 3 and f(3) = 24
Find C and a so that f(x) = Cax satisfies the given conditions.f(0) = 5 and for each unit increase in x, the output is multiplied by 1.5.
Find C and a so that f(x) = Cax satisfies the given conditions. f(0) = 10 and f(1) = 20
Find C and a so that f(x) = Cax satisfies the given conditions. f(0) = 7 and f(-1) = 1
Find C and a so that f(x) = Cax satisfies the given conditions. f(-1) = 8 and f(1) = 2
Combine the expressions by writing them as a logarithm of a single expression. log2 + log 3
Simplify ex e-2x.
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = |x-1|
Find C and a so that f(x) = Cax satisfies the given conditions.f(1) = 3 and for each unit increase in x, the output is multiplied by 3/4.
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = x³
Sketch a graph of y = f(x). Identify the domain of f. f(x) = 4(2)-*
How can you distinguish data that illustrate exponential growth from data that illustrate logarithmic growth?
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)
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = 1 1+x²
Find C and a so that f(x) = Cax satisfies the given conditions. f(1) = 9 and f(2) = 27
Combine the expressions by writing them as a logarithm of a single expression. log √2 + log V/2
Sketch a graph of y = f(x). Identify the domain of f. f(x) = 3x-1
Sketch a graph of y = f(x). Identify the domain of f. f(x) = log (x + 1)
Find C and a so that f(x) = Cax satisfies the given conditions. f(-2) = and f(2)= 12
Use the graph of f(x) = Cax to determine values for C and a. 5 y=fx) 3 2 1 0 l ܕܝ ܐ
Combine the expressions by writing them as a logarithm of a single expression. In 33 - In 11
Find a linear function f and an exponential function g whose graphs pass through the two given points. (-2, 12), (1, 1.5)
Use the fact that ax = ay implies x = y, to solve each equation. 52x = 5x-3
Combine the expressions by writing them as a logarithm of a single expression. log₂24 + log248
Find a linear function f and an exponential function g whose graphs pass through the two given points. (0.3). (1.2)
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = x¹/²
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x)=x^2/3
Use the fact that ax = ay implies x = y, to solve each equation. -X 7-x = 72x+1
Combine the expressions by writing them as a logarithm of a single expression. log4+ log 3 log 2
Use the graph of f(x) = Cax to determine values for C and a. -2 y = f(x) 0 12
Use the fact that ax = ay implies x = y, to solve each equation.
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = x² - 4x
Find a linear function f and an exponential function g whose graphs pass through the two given points. (1, 3), (5, 48)
Determine the final value of $1200 invested at 9% compounded semiannually for 3 years.
Decide if the situation could be modeled by a one-to-one function.The distance between the ground and a person who is riding a Ferris wheel after .x seconds
Find C and a so that f(x) = Cax models the situation described. State what the variable x represents in your formula.There are initially 5000 bacteria, and this sample doubles in size every hour.
Decide if the situation could be modeled by a one-to-one function.The cumulative numbers of AIDS cases from 1980 to 2010
Combine the expressions by writing them as a logarithm of a single expression. log75 + logik²
Let f(x) = x2 and g(x) = 1 - x and evaluate. (a) (f + g)(3) (c) (fg)(1) (b) (f- g)(-2) (d) (f/g)(3)
Greenhouse gases such as carbon dioxide trap heat from the sun. Presently, the net incoming solar radiation reaching Earth's surface is approximately 240 watts per square meter (W/m2). Any portion of
Use f(x) = x2 + 3x and g(x)=x-1 to find each expression. Identify its domain. (a) (ƒ + g)(x) (c) (fg)(x) (b) (f - g)(x) (d) (f/g)(x)
Find a function that models the data. Choose from exponential, logarithmic, or logistic functions. 2 y 0.25 3 0.86 0.86 4 2.19 2.19 5 3.57 3.57 6 4.23 7 4.43
Find a function that models the data. Choose from exponential, logarithmic, or logistic functions. x 2 y 0.08 3 4 5 6 1.30 2.16 2.83 3.38 7 3.84
Select an appropriate type of modeling function for the data shown in the graph. Choose from the following. i. Exponential ii. Logarithmic iii. Logistic
Find a function that models the data. Choose from exponential, logarithmic, or logistic functions.The table lists the actual or projected world population y (in billions) for selected years x. x
If f(x) = x2 and g(x) = 4x, (fg)(x) = _______.
State the inverse action or actions.Walking into a classroom, sitting down, and opening a book
Determine if f is one-to-one. You may want to graph y = f(x) and apply the horizontal line test. f(x) = 4 - ³x
Simplify the expression without a calculator. (5101)1/101
Describe verbally the inverse of the statement. Then express both the given statement and its inverse symbolically.Take the reciprocal of a nonzero number .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)
Tables for f and g are given. Evaluate each expression. r-20 2 4 f(x) 1 4 3 2 (a) (gof)(-2) x g(x) (b) (fog)(3) 12 3 4 2 4 -2 0 (c) f¹(3)
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 following table lists the number of new AIDS cases Cx years after 1980.(a) Find a function C(x) that models the data.(b) Graph C and the data. (c) Estimate the number of new cases in 1989.
Find (f ° g)(x) and identify its domain. f(x) = x³ = x² + 3x - 2 x² + - 3x-2 g(x) g(x) = x-¹
Find (f ° g)(x) and identify its domain. f(x)=√x +3 g(x) = 1 = x² -
Make a scatterplot of the data. Then find an exponential, logarithmic, or logistic function f that best models the data. x 1 y 2.0 2 1.6 3 1.3 4 1.0 5 0.82
Find (f ° g)(x) and identify its domain. ² + x² = (x) 8 1-x7A = (x)/
Simplify the expression without a calculator. (827)1/27
Expand the expression. If possible, write your answer without exponents. In xy
If f(x) = 5 - 2x, find f-1(x).
Find (f ° g)(x) and identify its domain. f(x) = 2 x-5 g(x)= 1 x+1
State the inverse action or actions.Opening the door and turning on the lights
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)
Describe verbally the inverse of the statement. Then express both the given statement and its inverse symbolically.Take the square root of a positive number x.
Determine if f is one-to-one. f(x) = 3x² - 2x + 1
The table is a complete representation of f. Use the table off to determine a table for f-1. Identify the domains and ranges off and f-1. x-1 6 0 4 46 3 1
Use the graph off to sketch a graph of f-1. (-4,-1) 3 (4,3) y = f(x) 3 1
Use the tables to evaluate the given expression. 0 1 2 f(x) 4 3 2 3 1 x g(x) 0 1 02 2 3 3 4

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