Chapter Review on Functions and Transformation and Inverse
Chapter
Chapter 2
Section
Chapter Review on Functions and Transformation and Inverse
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Solutions 55 Videos

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

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Q1a

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

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Q1b

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

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Q1c

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}

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Q2a

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

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Q2b

Simplify each expression and state any restrictions on x.

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

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Q3a

Simplify each expression and state any restrictions on x.

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

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Q3b

Simplify and state any restrictions.

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

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Q4a

Simplify and state any restrictions.

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

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Q4b

Simplify and state any restrictions.

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

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Q4c

Simplify and state any restrictions.

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

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Q4d

Simplify and state any restrictions.

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

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Q4e

Simplify and state any restrictions.

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

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Q4f

Simplify and state any restrictions.

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

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Q5a

Simplify and state any restrictions.

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

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Q5b

Simplify and state any restrictions.

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

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Q5c

Simplify and state any restrictions.

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

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Q5d

Simplify and state any restrictions.

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

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Q5e

Simplify and state any restrictions.

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

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Q5f

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

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

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Q6a

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

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

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Q6b

Repeat question 6 for each base function.

f(x) = x^2

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Q7i

Repeat question 6 for each base function.

f(x) = \sqrt x

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Q7ii

Repeat question 6 for each base function.

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

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Q7iii

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.

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Q8a

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.

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Q8b

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

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Q9a

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

f(x) = x^2 - 2

g(x) = x^2 - 2

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Q9b

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

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

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

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Q9c

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

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Q9d

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

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

g(x) = -f(x)

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Q10a

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

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

g(x) = -f(-x)

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Q10b

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

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

g(x) = -f(-x)

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Q10c

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)

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Q11a

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)

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Q11b

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)

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Q11c

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)

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Q11d

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

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Q12a

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

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Q12b

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}}

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Q12c

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}

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Q12d

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)

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Q13a

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

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Q13b

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

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Q13c

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

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Q13d

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)

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Q14a

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

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Q14b

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)]

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Q14c

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)

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Q14d

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.

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Q15a

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.

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Q15b

Determine an equation for the inverse of each function.

f(x) = -2x + 7

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Q16a

Determine an equation for the inverse of each function.

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

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Q16b

Determine an equation for the inverse of each function.

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

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Q16c

Determine an equation for the inverse of each function.

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

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Q16d