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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
Graph the linear function f on a domain of [−10, 10] for the function whose slope is 1/8 and y-intercept is 31/16. Label the points for the input values of −10 and 10.
If g(x) is the transformation of f(x) = x after a vertical compression by 1/3 , a shift left by 1, and a shift up by 3a. Write an equation for g(x).b. What is the slope of this line?c. Find the y-intercept of this line.
Graph the linear function f where f(x) = ax + b on the same set of axes on a domain of [−4, 4] for the following values of a and b.a. a = 2; b = 3 b. a = 2; b = 4 c. a = 2; b = −4 d. a = 2; b = −5
Graph the linear function f on a domain of [−0.1, 0.1] for the function whose slope is 75 and y-intercept is −22.5. Label the points for the input values of −0.1 and 0.1.
For the following exercises, write the equation of the line shown in the graph. --5-5-4-3-2 III 45 IIII X
For the following exercises, write the equation of the line shown in the graph. 3-4- -3 I 1 [I
For the following exercises, write the equation of the line shown in the graph. 10 -F--$-9 1-2 III + 45
Find the value of x if a linear function goes through the following points and has the following slope:(x, 2), (−4, 6), m = 3
For the following exercises, write the equation of the line shown in the graph. x K amb 1112 mb ééněkné
Find the value of y if a linear function goes through the following points and has the following slope:(10, y), (25, 100), m = −5
Find the equation of the line that passes through the following points:(a, b) and (a, b + 1)
For the following exercises, find the point of intersection of each pair of lines if it exists. If it does not exist, indicate that there is no point of intersection. y = - 3x + 4y = x + 1 +1 4 12
For the following exercises, find the point of intersection of each pair of lines if it exists. If it does not exist, indicate that there is no point of intersection. 2x - 3y = 5y + x = 12 30
For the following exercises, find the point of intersection of each pair of lines if it exists. If it does not exist, indicate that there is no point of intersection. 2x=y-3 y + 4x = 15
Find the equation of the line that passes through the following points:(2a, b) and (a, b + 1)
For the following exercises, find the point of intersection of each pair of lines if it exists. If it does not exist, indicate that there is no point of intersection. x-2y+2=3 x-y=3
Find the equation of the line that passes through the following points:(a, 0) and (c, d)
For the following exercises, find the point of intersection of each pair of lines if it exists. If it does not exist, indicate that there is no point of intersection. 5x+3y=-65 x - y = -5
At noon, a barista notices that she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves n more customers during her shift?
A gym membership with two personal training sessions costs $125, while gym membership with five personal training sessions costs $260. What is cost per session?
Find the equation of the line parallel to the line g(x) = −0.01x + 2.01 through the point (1, 2).
A clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30, while 3,000 shirts can be sold at a price of $22. Find a linear
Find the equation of the line perpendicular to the line g(x) = −0.01x + 2.01 through the point (1, 2).
A phone company charges for service according to the formula: C(n) = 24 + 0.1n, where n is the number of minutes talked, and C(n) is the monthly charge, in dollars. Find and interpret the rate of change and initial value.
For the following exercises, use the functions f(x) = −0.1x + 200 and g(x) = 20x + 0.1. Find the point of intersection of the lines f and g.
A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Find a linear relationship in the form y
For the following exercises, use the functions f(x) = −0.1x + 200 and g(x) = 20x + 0.1. Where is f(x) greater than g(x)? Where is g(x) greater than f(x)?
A city’s population in the year 1960 was 287,500. In 1989 the population was 275,900. Compute the rate of growth of the population and make a statement about the population rate of change in people per year.
A car rental company offers two plans for renting a car.Plan A: $30 per day and $0.18 per milePlan B: $50 per day with free unlimited mileage How many miles would you need to drive for plan B to save you money?
A town’s population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. Write an equation, P(t), for the population t years after 2003.
A cell phone company offers two plans for minutes. Plan A: $20 per month and $1 for every one hundred texts.Plan B: $50 per month with free unlimited texts. How many texts would you need to send per month for plan B to save you money?
Suppose that average annual income (in dollars) for the years 1990 through 1999 is given by the linear function: I(x) = 1,054x + 23,286, where x is the number of years after 1990. Which of the following interprets the slope in the context of the problem?a. As of 1990, average annual income was
A cell phone company offers two plans for minutes. Plan A: $15 per month and $2 for every 300 texts. Plan B: $25 per month and $0.50 for every 100 texts. How many texts would you need to send per month for plan B to save you money?
When temperature is 0 degrees Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the corresponding Fahrenheit temperature is 212. Express the Fahrenheit temperature as a linear function of C, the Celsius temperature, F(C).a. Find the rate of change of Fahrenheit
What is true of the appearance of graphs that reflect a direct variation between two variables?
What is the fundamental difference in the algebraic representation of a polynomial function and a rational function?
Explain the advantage of writing a quadratic function in standard form.
What is the difference between an x-intercept and a zero of a polynomial function f?
If division of a polynomial by a binomial results in a remainder of zero, what can be conclude?
Perform the indicated operation with complex numbers.(4 + 3i) + (−2 − 5i)
Explain the difference between the coefficient of a power function and its degree.
Explain how to add complex numbers.
Explain why we cannot find inverse functions for all polynomial functions.
If two variables vary inversely, what will an equation representing their relationship look like?
What is the fundamental difference in the graphs of polynomial functions and rational functions?
How can the vertex of a parabola be used in solving real world problems?
Explain why the Rational Zero Theorem does not guarantee finding zeros of a polynomial function.
If a polynomial function of degree n has n distinct zeros, what do you know about the graph of the function?
If a polynomial of degree n is divided by a binomial of degree 1, what is the degree of the quotient?
Perform the indicated operation with complex numbers.(6 − 5i) − (10 + 3i)
If a polynomial function is in factored form, what would be a good first step in order to determine the degree of the function?
What is the basic principle in multiplication of complex numbers?
Why must we restrict the domain of a quadratic function when finding its inverse?
Is there a limit to the number of variables that can jointly vary? Explain.
If the graph of a rational function has a removable discontinuity, what must be true of the functional rule?
Explain why the condition of a ≠ 0 is imposed in the definition of the quadratic function.
What is the difference between rational and real zeros?
Explain how the Intermediate Value Theorem can assist us in finding a zero of a function.
For the following exercises, use long division to divide. Specify the quotient and the remainder.(x2 + 5x − 1) ÷ (x − 1)
Perform the indicated operation with complex numbers.(2 − 3i)(3 + 6i)
In general, explain the end behavior of a power function with odd degree if the leading coefficient is positive.
Give an example to show the product of two imaginary numbers is not always imaginary.
When finding the inverse of a radical function, what restriction will we need to make?
For the following exercises, write an equation describing the relationship of the given variables.y varies directly as x and when x = 6, y = 12.
Can a graph of a rational function have no vertical asymptote? If so, how?
What is another name for the standard form of a quadratic function?
If Descartes’ Rule of Signs reveals a no change of signs or one sign of changes, what specific conclusion can be drawn?
Explain how the factored form of the polynomial helps us in graphing it.
For the following exercises, use long division to divide. Specify the quotient and the remainder.(2x2 − 9x − 5) ÷ (x − 5)
Perform the indicated operation with complex numbers. 2 − i/2 + i
What is the relationship between the degree of a polynomial function and the maximum number of turning points in its graph?
What is a characteristic of the plot of a real number in the complex plane?
The inverse of a quadratic function will always take what form?
For the following exercises, write an equation describing the relationship of the given variables.y varies directly as the square of x and when x = 4, y = 80.
Can a graph of a rational function have no x-intercepts? If so, how?
What two algebraic methods can be used to find the horizontal intercepts of a quadratic function?
If synthetic division reveals a zero, why should we try that value again as a possible solution?
If the graph of a polynomial just touches the x-axis and then changes direction, what can we conclude about the factored form of the polynomial?
For the following exercises, use long division to divide. Specify the quotient and the remainder.(3x2 + 23x + 14) ÷ (x + 7)
Solve the following equations over the complex number system.x2 − 4x + 5 = 0
What can we conclude if, in general, the graph of a polynomial function exhibits the following end behavior? As x → −∞, f(x) → −∞ and as x → ∞, f(x) → −∞.
For the following exercises, evaluate the algebraic expressions.If f(x) = x2 + x − 4, evaluate f(2i).
For the following exercises, find the inverse of the function on the given domain.f(x) = (x − 4)2 , [4, ∞)
For the following exercises, find the domain of the rational functions. f(x) = = x-1 x + 2
For the following exercises, write an equation describing the relationship of the given variables.y varies directly as the square root of x and when x = 36, y = 24.
For the following exercises, rewrite the quadratic functions in standard form and give the vertex.f(x) = x2 − 12x + 32
For the following exercises, use the Remainder Theorem to find the remainder. (x4 − 9x2 + 14) ÷ (x − 2)
For the following exercises, find the x- or t-intercepts of the polynomial functions. C(t) = 2(t − 4)(t + 1)(t − 6)
For the following exercises, use long division to divide. Specify the quotient and the remainder.(4x2 − 10x + 6) ÷ (4x + 2)
Solve the following equations over the complex number system.x2 + 2x + 10 = 0
For the following exercises, identify the function as a power function, a polynomial function, or neither.f(x) = x5
For the following exercises, evaluate the algebraic expressions.If f(x) = x3 − 2, evaluate f(i).
For the following exercises, find the inverse of the function on the given domain.f(x) = (x + 2)2 , [−2, ∞)
For the following exercises, write an equation describing the relationship of the given variables.y varies directly as the cube of x and when x = 36, y = 24.
For the following exercises, find the x- or t-intercepts of the polynomial functions.C(t) = 3(t + 2)(t − 3)(t + 5)
For the following exercises, use the Remainder Theorem to find the remainder.(3x3 − 2x2 + x − 4) ÷ (x + 3)
For the following exercises, find the domain of the rational functions. f(x) = x + 1 -
For the following exercises, rewrite the quadratic functions in standard form and give the vertex.g(x) = x2 + 2x − 3
For the following exercises, use long division to divide. Specify the quotient and the remainder. (6x² 25x25) ÷ (6x + 5)
For the following exercises, write the quadratic function in standard form. Then, give the vertex and axes intercepts. Finally, graph the function.f(x) = x2 − 4x − 5
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