Determine if the functions in each pair are equivalent.

f(x) = -4(x^2 + x - 2) + (2x - 3)^2, g(x) = x^2 - 16x + 17

Determine if the functions in each pair are equivalent.

f(x) = 5(x ^2 + 2x - 3) - (2x + 5)(-x + 1), g(x) = 7x^2 + 13x - 20

Determine if the functions in each pair are equivalent.

f(x) = (x + 5)^2 - 2(3 - x)(x + 1), g(x) = -2(-x^2 + 4x - 8) + (x + 4)^2 - 6

State the restrictions on f(x). Then determine whether g(x) is the simplified version of f(x). If not, determine the proper simplified version.

f(x) = \dfrac{8x^2 + 10x - 3}{4x^2 - x}

g(x) = \dfrac{2x + 3}{x}

State the restrictions on f(x). Then determine whether g(x) is the simplified version of f(x). If not, determine the proper simplified version.

f(x) = \dfrac{8x^2 - 12x - 8}{4x^2 - 8x}

g(x) = 2x + 1

Simplify each expression and state any restrictions on x.

\dfrac{x + 8}{x^2 + 10x + 16}

Simplify each expression and state any restrictions on x.

\dfrac{8x^2 - 6x - 9}{4x^2 + 27x + 18}

Simplify and state any restrictions.

\dfrac{64a^2b}{21ab^2} \times \dfrac{63a^3b^3}{8a^2b}

Simplify and state any restrictions.

\dfrac{54a^3b^2}{81c^2} \div \dfrac{108a^2b}{45c}

Simplify and state any restrictions.

\dfrac{3x - 4}{x + 9} \times \dfrac{2x + 18}{3x - 4}

Simplify and state any restrictions.

\dfrac{x^2 - 5x - 24}{x^2 - 2x - 15} \times \dfrac{x - 5}{x + 4}

Simplify and state any restrictions.

\dfrac{x - 4}{x - 3} \div \dfrac{4 - x}{2x - 6}

Simplify and state any restrictions.

\dfrac{x^2 + 11 x + 24}{x^2 + 2x - 3} \div \dfrac{x - 8}{x - 1}

Simplify and state any restrictions.

\dfrac{2}{3x} + \dfrac{3}{5x}

Simplify and state any restrictions.

\dfrac{2 - a}{6ab} + \dfrac{7 + b}{12b^2}

Simplify and state any restrictions.

\dfrac{x + 10}{x - 1} + \dfrac{x - 3}{x + 2}

Simplify and state any restrictions.

\dfrac{8x - 3}{x^2 - 7x + 12} - \dfrac{2x + 1}{x - 4}

Simplify and state any restrictions.

\dfrac{4x + 1}{x + 3} + \dfrac{x - 6}{x^2 - 9}

Simplify and state any restrictions.

\dfrac{5x + 25}{x^2 + 7x + 10} + \dfrac{10x - 20}{x^2 - 4}

Use the base function f(x) = x. Write the equation for each transformed function.

s(x) = f(x + 2) - 8

Use the base function f(x) = x. Write the equation for each transformed function.

(x) = f(x - 5) + 1

Repeat question 6 for each base function.

f(x) = x^2

Repeat question 6 for each base function.

f(x) = \sqrt x

Repeat question 6 for each base function.

f(x) = \dfrac{1}{x}

Each graph represents a transformation of one of the base functions f(x) = x, f(x) = x^2, f(x) = \sqrt x, or f(x) = \dfrac{1}{x}. State the base function and the equation of the transformed function.

Each graph represents a transformation of one of the base functions f(x) = x, f(x) = x^2, f(x) = \sqrt x, or f(x) = \dfrac{1}{x}. State the base function and the equation of the transformed function.

Determine if g(x) is a reflection of f(x). Justify your answer.

f(x) = \sqrt {x - 13} + 6

g(x) = -\sqrt {13 - x} - 6

Determine if g(x) is a reflection of f(x). Justify your answer.

f(x) = x^2 - 2

g(x) = x^2 - 2

Determine if g(x) is a reflection of f(x). Justify your answer.

f(x) = \sqrt {x + 7}

g(x) = \sqrt {x - 7}

Determine if g(x) is a reflection of f(x). Justify your answer.

f(x) = \dfrac{1}{x + 15} - 8

f(x) = -\dfrac{1}{x + 15} + 8

For each function f(x), determine the equation for g(x).

f(x) = \sqrt {x - 1} + 8

g(x) = -f(x)

For each function f(x), determine the equation for g(x).

f(x) = (x - 3)^2 + 10

g(x) = -f(-x)

For each function f(x), determine the equation for g(x).

f(x) = \dfrac{1}{x + 7} - 2

g(x) = -f(-x)

For each function g(x), identify the value of a or k and describe how the graph of g(x) can be obtained from the graph of f(x).

g(x) = 9f(x)

For each function g(x), identify the value of a or k and describe how the graph of g(x) can be obtained from the graph of f(x).

g(x) = f(3x)

For each function g(x), identify the value of a or k and describe how the graph of g(x) can be obtained from the graph of f(x).

g(x) = \dfrac{2}{5} f(x)

For each function g(x), identify the value of a or k and describe how the graph of g(x) can be obtained from the graph of f(x).

g(x) = f(\dfrac{1}{7} x)

For each function g(x), describe the transformation from a base function of f(x) = x, f(x) = x^2, f(x) = \sqrt x, or f(x) = \dfrac{1}{x}. Then transform the graph of f(x) to sketch a graph of g(x).

g(x) = 13x

For each function g(x), describe the transformation from a base function of f(x) = x, f(x) = x^2, f(x) = \sqrt x, or f(x) = \dfrac{1}{x}. Then transform the graph of f(x) to sketch a graph of g(x).

g(x) = (5x)^2

For each function g(x), describe the transformation from a base function of f(x) = x, f(x) = x^2, f(x) = \sqrt x, or f(x) = \dfrac{1}{x}. Then transform the graph of f(x) to sketch a graph of g(x).

g(x) = \sqrt {\dfrac{x}{3}}

For each function g(x), describe the transformation from a base function of f(x) = x, f(x) = x^2, f(x) = \sqrt x, or f(x) = \dfrac{1}{x}. Then transform the graph of f(x) to sketch a graph of g(x).

g(x) = \dfrac{6}{x}

Compare the transformed equation to y = af[k(x - d)] + c to determine the values of the parameters a, k, d, and c. Then describe, in the appropriate order, the transformations that must be applied to a base function f(x) to obtain the transformed function.

g(x) = 7f(x -1)

Compare the transformed equation to y = af[k(x - d)] + c to determine the values of the parameters a, k, d, and c. Then describe, in the appropriate order, the transformations that must be applied to a base function f(x) to obtain the transformed function.

g(x) = \dfrac{1}{5} f(x) - 3

Compare the transformed equation to y = af[k(x - d)] + c to determine the values of the parameters a, k, d, and c. Then describe, in the appropriate order, the transformations that must be applied to a base function f(x) to obtain the transformed function.

g(x) = f(x + 9) + 8

Compare the transformed equation to y = af[k(x - d)] + c to determine the values of the parameters a, k, d, and c. Then describe, in the appropriate order, the transformations that must be applied to a base function f(x) to obtain the transformed function.

g(x) = f(\dfrac{1}{2}x) + 10

Given each base function f(x), write the equation of the transformed function g(x). Then transform the graph of f(x) to sketch a graph of g(x).

f(x) = \sqrt x

g(x) = 3f(2x)

Given each base function f(x), write the equation of the transformed function g(x). Then transform the graph of f(x) to sketch a graph of g(x).

f(x) = \dfrac{1}{x}

g(x) = f(x - 4) + 9

Given each base function f(x), write the equation of the transformed function g(x). Then transform the graph of f(x) to sketch a graph of g(x).

f(x) = x^2

g(x) = f[\dfrac{1}{4}(x + 5)]

Given each base function f(x), write the equation of the transformed function g(x). Then transform the graph of f(x) to sketch a graph of g(x).

f(x) = x

g(x) = -2f(x - 7)

Copy each graph of f(x). Then sketch the inverse of each function, and state the domain and range of the function and of its inverse.

Copy each graph of f(x). Then sketch the inverse of each function, and state the domain and range of the function and of its inverse.

Determine an equation for the inverse of each function.

f(x) = -2x + 7

Determine an equation for the inverse of each function.

f(x) = \dfrac{5x - 3}{4}

Determine an equation for the inverse of each function.

f(x) = (x - 3)^2 + 1

Determine an equation for the inverse of each function.

f(x) = -\dfrac{1}{4} x^2 + 9