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- Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated. See Examples 4–6. 2-i and 6-3i
Problem 73
Problem 73
Graph each rational function. See Examples 5–9. ƒ(x)=(3x^2+3x-6)/(x^2-x-12)
Problem 73a
Solve each problem. Work each of the following. Sketch the graph of a function that does not intersect its horizontal asymptote y=1, has the line x=3 as a vertical asymptote, and has x-intercepts (2, 0) and (4, 0).
Problem 73b
Solve each problem. Work each of the following. Find an equation for a possible corresponding rational function.
Problem 74b
Solve each problem. Work each of the following. Find an equation for a possible corresponding rational function.
Problem 75b
Solve each problem. Find a rational function ƒ having the graph shown.
Problem 76
Graph each rational function. See Examples 5–9.
Problem 76a
Solve each problem. This rational function has two holes and one vertical asymptote.
What are the x-values of the holes?
- Perform each division. See Examples 7 and 8. (9y2+12y-5)/(3y)
Problem 79
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=2x^3-4x^2+2x+7
Problem 79
Problem 80
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=x3+2x2+x-10
- Perform each division. See Examples 7 and 8. (15m^3+25m^2+30m)/(5m^3)
Problem 81
- Find a value of c so that y = x^2 - 10x + c has exactly one x-intercept.
Problem 81
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=4x^3-x^2+2x-7
Problem 81
- For what values of a does y = ax^2 - 8x + 4 have no x-intercepts?
Problem 82
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=3x^3+6x^2+x+7
Problem 82
Problem 82
Graph each rational function. See Examples 5–9. ƒ(x)=[(x-5)(x-2)]/(x^2+9)
- Perform each division. See Examples 7 and 8. (-4x^7-14x^6+10x^4-14x^2)/(-2x^2)
Problem 83
- Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=2x^3-5x^2-x+1; [-1, 0]
Problem 83
- Define the quadratic function ƒ having x-intercepts (2, 0) and (5, 0) and y-intercept (0, 5).
Problem 83
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=5x^4+3x^2+2x-9
Problem 83
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=3x^4+2x^3-8x^2-10x-1
Problem 84
- Define the quadratic function ƒ having x-intercepts (1, 0) and (-2, 0) and y-intercept (0, 4).
Problem 84
- Perform each division. See Examples 7 and 8. (-4m^2n^2-21mn^3+18mn^2)/(-14m^2n^3)
Problem 85
- The distance between the two points P(x₁, y₁) and R(x₂, y₂) is d(P, R) = √(x₁ - x₂)^2 + (y₁ -y₂)^2. Distance formula. Find the closest point on the line y = 2x to the point (1, 7). (Hint: Every point on y = 2x has the form (x, 2x), and the closest point has the minimum distance.)
Problem 85
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=-8x^4+3x^3-6x^2+5x-7
Problem 85
- Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=2x^3-5x^2-x+1; [1.4, 2]
Problem 85
- A quadratic equation ƒ(x) = 0 has a solution x = 2. Its graph has vertex (5, 3). What is the other solution of the equation?
Problem 86
- Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=6x^4+2x^3+9x^2+x+5
Problem 86
- Perform each division. See Examples 7 and 8. (8wxy^2+3wx^2y+12w^2xy)/(4wx^2y)
Problem 87
