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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

How can the logarithmic equation logb x = y be solved for x using the properties of exponents?
The graph of is reflected about the y-axis and compressed vertically by a factor of 1/5. What is the equation of the new function, g(x)? State its y-intercept, domain, and range. X- (1) = (x)F
For the following exercises, use like bases to solve the exponential equation.4−3v−2 = 4−v
Discuss the meaning of the common logarithm. What is its relationship to a logarithm with base b, and how does the notation differ?
For the following exercises, identify whether the statement represents an exponential function. Explain.The average annual population increase of a pack of wolves is 25.
For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.ln(3ab · 5c)
Does the graph of a general logarithmic function have a horizontal asymptote? Explain.
The graph of f(x) = 10x is reflected about the x-axis and shifted upward 7 units. What is the equation of the new function, g(x)? State its y-intercept, domain, and range.
For the following exercises, use like bases to solve the exponential equation.64 ⋅ 43x = 16
For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. log 13 17
Discuss the meaning of the natural logarithm. What is its relationship to a logarithm with base b, and how does the notation differ?
For the following exercises, identify whether the statement represents an exponential function. Explain.A population of bacteria decreases by a factor of 1/8 every 24 hours.
For the following exercises, state the domain and range of the function.f(x) = log3 (x + 4)
The graph of f(x) = (1.68)x is shifted right 3 units, stretched vertically by a factor of 2, reflected about the x-axis, and then shifted downward 3 units. What is the equation of the new function,
For the following exercises, use like bases to solve the exponential equation.32x+1 ⋅ 3x = 243
For the following exercises, rewrite each equation in exponential form. log4 (q) = m
For the following exercises, identify whether the statement represents an exponential function. Explain.The value of a coin collection has increased by 3.25% annually over the last 20 years.
For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. X log, z W
For the following exercises, state the domain and range of the function.h(x) = ln (1/2 − x)
The graph of + 4 is shifted downward 4 units, and then shifted left 2 units, stretched vertically by a factor of 4, and reflected about the x-axis. What is the equation of the new function,
For the following exercises, use like bases to solve the exponential equation.2−3n ⋅ 1/4 = 2n+2
For the following exercises, rewrite each equation in exponential form.loga (b) = c
For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. In 4k
For the following exercises, identify whether the statement represents an exponential function. Explain.For each training session, a personal trainer charges his clients $5 less than the previous
For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.log2 (yx)
For the following exercises, state the domain and range of the function.g(x) = log5 (2x + 9) − 2
For the following exercises, use like bases to solve the exponential equation.625 ⋅ 53x+3 = 125
For the following exercises, graph the function and its reflection about the y-axis on the same axes, and give the y-intercept. X f(x) = 3 ( 1²1 ) 2
For the following exercises, rewrite each equation in exponential form.log16(y) = x
For the following exercises, identify whether the statement represents an exponential function. Explain.The height of a projectile at time t is represented by the function h(t) = −4.9t 2 + 18t + 40.
For the following exercises, condense to a single logarithm if possible.ln(7) + ln(x) + ln(y)
For the following exercises, state the domain and range of the function.h(x) = ln(4x + 17) − 5
For the following exercises, use like bases to solve the exponential equation.363b/362b = 2162−b
For the following exercises, graph the function and its reflection about the y-axis on the same axes, and give the y-intercept.g(x) = −2(0.25)x
For the following exercises, rewrite each equation in exponential form.logx (64) = y
For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function A(t) = 115(1.025)t. In a neighboring forest, the population of
For the following exercises, condense to a single logarithm if possible.log3 (2) + log3 (a) + log3 (11) + log3 (b)
For the following exercises, use like bases to solve the exponential equation.(1/64)3n ⋅ 8 = 26
For the following exercises, graph the function and its reflection about the y-axis on the same axes, and give the y-intercept.h(x) = 6(1.75)−x
For the following exercises, rewrite each equation in exponential form.logy (x) = −11
For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function A(t) = 115(1.025)t . In a neighboring forest, the population
For the following exercises, graph each set of functions on the same axes. f(x) = 3(1), 8( : 1, g(x) = 3(2)x, and h(x) = 3(4)*
For the following exercises, condense to a single logarithm if possible.logb (28) − logb (7)
For the following exercises, state the domain and the vertical asymptote of the function.f(x) = logb (x − 5)
For the following exercises, use logarithms to solve.9x−10 = 1
For the following exercises, graph each set of functions on the same axes. = ¹(3), g(x) = 2(3), and h(x) = 4(3)* f(x) =
For the following exercises, rewrite each equation in exponential form.log15(a) = b
For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function A(t) = 115(1.025)t. In a neighboring forest, the population of
For the following exercises, state the domain and the vertical asymptote of the function.g(x) = ln(3 − x)
For the following exercises, use logarithms to solve.2e6x = 13
For the following exercises, condense to a single logarithm if possible. -log, (+/-)
For the following exercises, rewrite each equation in exponential form.logy (137) = x
For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function A(t) = 115(1.025)t. In a neighboring forest, the population of
For the following exercises, match each function with one of the graphs in Figure 12.f(x) = 2(0.69)x Figure 12
For the following exercises, state the domain and the vertical asymptote of the function.f(x) = log(3x + 1)
For the following exercises, use logarithms to solve.er+10 − 10 = −42
For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function A(t) = 115(1.025)t. In a neighboring forest, the population of
For the following exercises, match each function with one of the graphs in Figure 12.f(x) = 2(1.28)x Figure 12
For the following exercises, rewrite each equation in exponential form.log13(142) = a
For the following exercises, condense to a single logarithm if possible.1/3 ln(8)
For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. log X513
For the following exercises, state the domain and the vertical asymptote of the function.f(x) = 3log(−x) + 2
For the following exercises, use logarithms to solve.2 ⋅ 109a = 29
For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. In a b-4 2 5
For the following exercises, match each function with one of the graphs in Figure 12.f(x) = 2(0.81)x Figure 12
For the following exercises, rewrite each equation in exponential form.log(v) = t
For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain.y = 300(1 − t)5
For the following exercises, state the domain and the vertical asymptote of the function.g(x) = −ln(3x + 9) − 7
For the following exercises, match each function with one of the graphs in Figure 12.f(x) = 4(1.28)x Figure 12
For the following exercises, use logarithms to solve.−8 ⋅ 10p+7 − 7 = −24
For the following exercises, rewrite each equation in exponential form.ln(w) = n
For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain.y = 220(1.06)x
For the following exercises, state the domain, vertical asymptote, and end behavior of the function.f(x) = ln(2 − x)
For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. log(√x³ y 4)
For the following exercises, state the domain, vertical asymptote, and end behavior of the function. f(x) = log( X 3 7
For the following exercises, use logarithms to solve.7e3n−5 + 5 = −89
For the following exercises, rewrite each equation in logarithmic form.4x = y
For the following exercises, match each function with one of the graphs in Figure 12.f(x) = 2(1.59)x B Figure 12
For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain.y = 16.5(1.025)1/x
For the following exercises, use logarithms to solve.e−3k + 6 = 44
For the following exercises, rewrite each equation in logarithmic form.cd = k
For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain.y = 11,701(0.97)t
For the following exercises, use the graphs to write an equation for the function. 160.000 -10-8-6-4 y 54 1 100 6 8 10 IT
For the following exercises, use a calculator with CAS to answer the questions. Consider with k = 1, 2, 3. What do you expect x x-1 the result to be ifk = 4?
For the following exercises, use the given information to answer the questions.The force exerted by the wind on a plane surface varies jointly with the square of the velocity of the wind and with the
For the following exercises, use a calculator with CAS to answer the questions. Consider x²-k¹ x-k expect the result to be if k = 4? for k= 1, 2, 3. What do you
For the following exercises, determine the function described and then use it to answer the question.An object dropped from a height of 200 meters has a height, h(t), in meters after t seconds have
For the following exercises, sketch a graph of the quadratic function and give the vertex, axis of symmetry, and intercepts.f(x) = x2 − 7x + 3
For the following exercises, sketch a graph of the quadratic function and give the vertex, axis of symmetry, and intercepts.f(x) = x2 − 5x − 6
For the following exercises, use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm which of those possibilities is the actual
For the following exercises, solve the application problem.The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. A cylinder contains oxygen at a
For the following exercises, use the given information to answer the questions.The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is
For the following exercises, use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm which of those possibilities is the actual
For the following exercises, solve the application problem. The weight of an object above the surface of the earth varies inversely with the distance from the center of the earth.If a person
For the following exercises, sketch a graph of the quadratic function and give the vertex, axis of symmetry, and intercepts. f(x) = x2 − 2x
For the following exercises, graph the polynomial functions using a calculator. Based on the graph, determine the intercepts and the end behavior.f(x) = x(14 − 2x)(10 − 2x)
For the following exercises, use the graph to identify zeros and multiplicity. I #
For the following exercises, write an equation for a rational function with the given characteristics.Vertical asymptotes at x = −4 and x = −5, x-intercepts at (4, 0) and (−6, 0), horizontal
For the following exercises, use synthetic division to find the quotient and remainder. ¹-22 x+2
For the following exercises, use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm which of those possibilities is the actual

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