Chapter Review on Functions and Transformation and Inverse
Chapter
Chapter 2
Section
Chapter Review on Functions and Transformation and Inverse
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

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

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

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}

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

Q2b

Simplify each expression and state any restrictions on x.

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

Q3a

Simplify each expression and state any restrictions on x.

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

Q3b

Simplify and state any restrictions.

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

Q4a

Simplify and state any restrictions.

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

Q4b

Simplify and state any restrictions.

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

Q4c

Simplify and state any restrictions.

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

Q4d

Simplify and state any restrictions.

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

Q4e

Simplify and state any restrictions.

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

Q4f

Simplify and state any restrictions.

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

Q5a

Simplify and state any restrictions.

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

Q5b

Simplify and state any restrictions.

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

Q5c

Simplify and state any restrictions.

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

Q5d

Simplify and state any restrictions.

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

Q5e

Simplify and state any restrictions.

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

Q5f

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

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

Q6a

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

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

Q6b

Repeat question 6 for each base function.

f(x) = x^2

Q7i

Repeat question 6 for each base function.

f(x) = \sqrt x

Q7ii

Repeat question 6 for each base function.

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

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.

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.

Q8b

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

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

Q9a

f(x) = x^2 - 2

g(x) = x^2 - 2

Q9b

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

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

Q9c

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

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

Q9d

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

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

g(x) = -f(x)

Q10a

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

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

g(x) = -f(-x)

Q10b

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

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

g(x) = -f(-x)

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)

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)

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)

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)

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

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

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}}

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}

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)

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

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

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

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)

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

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)]

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)

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.

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.

Q15b

Determine an equation for the inverse of each function.

f(x) = -2x + 7

Q16a

Determine an equation for the inverse of each function.

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

Q16b

Determine an equation for the inverse of each function.

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

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