Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=5x^3+7x^2-x+9$

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $x^2-4x\ge 0$

In Exercises 19–24, (a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Determine whether the graph has y-axis symmetry, origin symmetry, or neither. (c) Graph the function. $f\left(x\right)=x^3-x^2-9x+9$

Divide using synthetic division. (3x²+7x−20)÷(x+5)

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=11x^3-6x^2+x+3$

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation.

In Exercises 19–24, (a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Determine whether the graph has y-axis symmetry, origin symmetry, or neither. (c) Graph the function. $f\left(x\right)=4x-x^3$

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as z and inversely as the sum of y and w.

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $2x^2+3x>0$

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. f(x)=x/(x+4)

Divide using synthetic division. (4x³−3x²+3x−1)÷(x−1)

In Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quotient from part (b) to find the remaining roots and solve the equation. 6x³+25x²−24x+5=0

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. y−1=(x−3)²

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=5x^4+7x^2-x+9$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. f(x)=11x⁴−6x²+x+3

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 3x² − 5x ≤ 0

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2(x+2)²−1

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=-5x^4+7x^2-x+9$

Divide using synthetic division. (6x⁵−2x³+4x²−3x+1)÷(x−2)

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. −x² + x ≥ 0

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. g(x)=(x+3)/x(x+4)

In Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quotient from part (b) to find the remaining roots and solve the equation. x⁴−2x³−5x²+8x+4=0

Divide using synthetic division. (x⁵+4x⁴−3x²+2x+3)÷(x−3)

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. −x² + 2x ≥ 0

In Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=-11x^4-6x^2+x+3$

In Exercises 25–26, graph each polynomial function. $f\left(x\right)=2x^2(x-1{)}^3(x+2)$

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=3; 1 and 5i are zeros; f(-1) = -104

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=4−(x−1)²

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=2(x−5)(x+4)²

Divide using synthetic division. (x²−5x−5x³+x⁴)÷(5+x)