Find the domain of each rational function. f(x)=(x+7)/(x²+49)

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+5x+4>0

The graph of a quadratic function is given. Write the function's equation, selecting from the following options.

$f\left(x\right)=x^2+2x+1g\left(x\right)=x^2-2x+1$

$h\left(x\right)=x^2-1j\left(x\right)=-x^2-1$

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as x and z. y = 25 when x = 2 and z = 5. Find y when x = 8 and z = 12.

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=x^1/3 −4x²+7

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as a and b and inversely as the square root of c. y = 12 when a = 3, b = 2, and c = 25. Find y when a = 5, b = 3 and c = 9.

Determine which functions are polynomial functions. For those that are, identify the degree. $f\left(x\right)=(x^2+7)/x^3$

In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=x³+x²−4x−4

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. x²−6x+9<0

Among all pairs of numbers whose difference is 14, find a pair whose product is as small as possible. What is the minimum product?

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2(x−3)²+1

Divide using long division. State the quotient, and the remainder, $r\left(x\right)$. $\frac{2x^3 + 7x^2 + 9x - 20}{x + 3}$

Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.

As $x\to -3^{-}$, $f\left(x\right)\to$____

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (3x²−2x+5)/(x−3)

Determine which functions are polynomial functions. For those that are, identify the degree. $f\left(x\right)=(x^2+7)/3$

In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=x³−2x²−11x+12

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] $f\left(x\right)=-x^3+x^2+2x$

a.b. c. d.

Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.

As $x\to 1^{-},f\left(x\right){\to }_{{}_{}}$______

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=−2(x+1)²+5

Identify which graphs are not those of polynomial functions.

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).]

$f\left(x\right)=x^6-6x^4+9x^2$

In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=2x³−3x²−11x+6

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z.

Divide using long division. State the quotient, and the remainder, r(x). (4x⁴−4x²+6x)/(x−4)

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+10x−8≤0

Divide using long division. State the quotient, and the remainder, r(x). (x⁴−81)/(x−3)

Identify which graphs are not those of polynomial functions.

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. 9x²+3x−2≥0

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2x²−8x+3

Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.

As $x\to -\infty ,f\left(x\right){\to }_{{}_{}}$_____