- Provide a short answer to each question. What is the domain of the function ƒ(x)=1/x? What is its range?
Problem 1
- Determine whether each statement is true or false. If false, explain why. Because x-1 is a factor of ƒ(x)=x^6-x^4+2x^2-2, we can also conclude that ƒ(1)=0
Problem 1
Problem 2
Provide a short answer to each question. What is the domain of the function ? What is its range?
Problem 3
Fill in the blank(s) to correctly complete each sentence, or answer the question as appropriate. In the equation y = 6x, y varies directly as x. When x=5, y=30. What is the value of y when x=10?
Problem 3
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) = 0

- Determine whether each statement is true or false. If false, explain why. For ƒ(x)=(x+2)^4(x-3), the number 2 is a zero of multiplicity 4.
Problem 3
- Fill in the blank(s) to correctly complete each sentence. The highest point on the graph of a parabola that opens down is the ____ of the parabola.
Problem 3
- Graph each quadratic function. Give the vertex, axis, x-intercepts, y-intercept, domain, range, and largest open intervals of the domain over which each function is increasing or decreasing. ƒ(x)=-3x^2-12x-1
Problem 3
Problem 4
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) < 0

Problem 5
Using k as the constant of variation, write a variation equation for each situation. h varies inversely as t.
Problem 5
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) > 0

- Determine whether each statement is true or false. If false, explain why. A polynomial function having degree 6 and only real coefficients may have no real zeros.
Problem 5
- Fill in the blank(s) to correctly complete each sentence. The vertex of the graph of ƒ(x) = x^2 + 2x + 4 has x-coordinate ____ .
Problem 5
Problem 6
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 7x(x - 1)(x - 2) ≥ 0

Problem 6
Determine whether each statement is true or false. If false, explain why. The polynomial function has three variations in sign.
Problem 7
Solve each problem. If y varies directly as x, and y=20 when x=4, find y when x = -6.
- Use synthetic division to perform each division. (x^3 + 3x^2 +11x + 9) / x+1
Problem 7
Problem 7
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(X-2) / {(X-1)(X-3)} = 0

- Provide a short answer to each question. Is ƒ(x)=1/x^2 an even or an odd function? What symmetry does its graph exhibit?
Problem 7
Problem 7a
Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by , where between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is modeled by . Find the number of volunteers in each of the following months.
January
Problem 7b
Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by , where between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, is modeled by . Find the number of volunteers in each of the following months.
May
Problem 7c
Solve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by where between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, is modeled by . Find the number of volunteers in each of the following months.
August
Problem 7d
Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by , where between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, is modeled by . Find the number of volunteers in each of the following months.
October
Problem 7e
Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by , where between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, is modeled by . Find the number of volunteers in each of the following months.
December
Problem 7f
Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by , where between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, is modeled by . Find the number of volunteers in each of the following months. Sketch a graph of for January through December. In what month are the fewest volunteers available?
Problem 8
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(X-2) / {(X-1)(X-3)} < 0

Problem 8
Determine whether each statement is true or false. If false, explain why. The product of a complex number and its conjugate is always a real number.
Problem 9
Solve each problem. If m varies jointly as x and y, and m=10 when x=2 and y=14, find m when x=21 and y=8.
- Use synthetic division to perform each division. (5x^4 +5x^3 + 2x^2 - x-3) / x+1
Problem 9
Problem 9
Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(X-2) / {(X-1)(X-3)} > 0

Ch. 3 - Polynomial and Rational Functions
