Chapter Review
Chapter
Chapter 2
Section
Chapter Review
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Solutions 45 Videos

Determine whether the functions in pair are equivalent.

\displaystyle f(x) = (x +6)(x - 8) + (x + 16)(x + 3)

\displaystyle g(x) = 3(x^2 + 3x + 5) -(x -5)(x - 3)

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Q1a

Determine whether the functions in pair are equivalent.

\displaystyle f(x) = (x + 5)(x -4) -(x -8)(x -1)

\displaystyle g(x) = 2(5x - 28)

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Q1b

Simplify each expression and state all restrictions on x.

\displaystyle \frac{x + 7}{x^2 + 10x + 21}

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Q2a

Simplify each expression and state all restrictions on x.

\displaystyle \frac{x^2 - 64}{x -8}

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Q2b

A square piece of cardboard with side length 40 cm is used to create an open-topped box by cutting out squares with side length x from each corner.

a) Determine a simplified expression for the surface area of the box.

b) Determine any restrictions on the value of x.

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Q3

Simplify the expression and state the restrictions.

\displaystyle \frac{3x^2 }{5xy} \times \frac{20xy^3}{12 xy}

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Q4a

Simplify the expression and state the restrictions.

\displaystyle \frac{15a^3b^4}{20a^2b} \div \frac{6b}{8ab^2}

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Q4b

Simplify the expression and state the restrictions.

\displaystyle \frac{1}{3x} + \frac{5}{2x^2}

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Q4c

Simplify the expression and state the restrictions.

\displaystyle \frac{4}{x-6} - \frac{3}{x -4}

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Q4d

Simplify the expression and state the restrictions.

\displaystyle \frac{x^2 + 7x}{3x + 21} \times \frac{x^2 + 3x + 2}{x + 2}

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Q5a

Simplify the expression and state the restrictions.

\displaystyle \frac{x^2 + 4x -60}{3x + 30} \div \frac{x^2 -8x + 12}{6x -12}

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Q5b

Simplify the expression and state the restrictions.

\displaystyle \frac{3}{x^2 + 7x +10} - \frac{5x}{x^2 -4}

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Q5c

Simplify the expression and state the restrictions.

\displaystyle \frac{-10x}{x^2 +18x + 32} + \frac{12x}{x^2 + 6x -160}

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Q5d

A square piece of cardboard with side length 40 cm is used to create an open-topped box by cutting out squares with side length x from each corner.

Determine a simplified expression for the ratio of the volume to the surface area. What are the restrictions on x?

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Q6

Copy the graph of the function f(x). Sketch the graph of g(x) by determining the image points A', B’, C', and D'.

g(x) = f(x) +6

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Q7a

Copy the graph of the function f(x). Sketch the graph of g(x) by determining the image points A', B’, C', and D'.

g(x) = f(x-3)

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Q7b

Let f(x) = x^2.

  • Express g(x) = f(x -d) + c.
  • Sketch g(x).
  • State the Domain and Range.

g(x) = (x + 7)^2 -8

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Q8a

Let f(x) = x^2.

  • Express g(x) = f(x -d) + c.
  • Sketch g(x).
  • State the Domain and Range.

g(x) = \sqrt{x -6} + 3

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Q8b

Let f(x) = x^2.

  • Express g(x) = f(x -d) + c.
  • Sketch g(x).
  • State the Domain and Range.

g(x) = \frac{1}{x + 3}+ 1

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Q8c

Copy the graph of f(x) and sketch g(x)). State the domain and range of each function.

g(x) = f(-x)

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Q9a

Copy the graph of f(x) and sketch g(x)). State the domain and range of each function.

g(x) = -f(x)

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Q9b

Copy the graph of f(x) and sketch g(x)). State the domain and range of each function.

g(x) = -f(-x)

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Q9c

Determine the equation of each function, g(x), after a reflection in the x-axis.

  • i) f(x) = \sqrt{x} + 5
  • ii) f(x) =\frac{1}{x} - 7
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Q10a

Determine the equation of each function h(x), after a reflection in the y—axis.

  • i) f(x) = \sqrt{x} + 5
  • ii) f(x) =\frac{1}{x} - 7
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Q10b

Given the function f(x) =x^2, identify the value of a or k, transform the graph of f(x) to sketch the graph of g(x), and state the domain and range of the function.

g(x) = 4f(x)

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Q11a

Given the function f(x) =x^2, identify the value of a or k, transform the graph of f(x) to sketch the graph of g(x), and state the domain and range of the function.

g(x) = f(5x)

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Q11b

Given the function f(x) =x^2, identify the value of a or k, transform the graph of f(x) to sketch the graph of g(x), and state the domain and range of the function.

g(x) = f(\frac{x}{3})

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Q11c

Given the function f(x) =x^2, identify the value of a or k, transform the graph of f(x) to sketch the graph of g(x), and state the domain and range of the function.

g(x) = \frac{1}{4}f(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) =\frac{1}{x}.

Then, transform the graph of f(x) to sketch the graph of g(x).

g(x) =5x

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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) =\frac{1}{x}.

Then, transform the graph of f(x) to sketch the graph of g(x).

g(x) = \frac{1}{4x}

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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) =\frac{1}{x}.

Then, transform the graph of f(x) to sketch the graph of g(x).

g(x) = (3x)^2

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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) =\frac{1}{x}.

Then, transform the graph of f(x) to sketch the graph of g(x).

g(x) = \sqrt{9x}

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Q12d

Describe, in the appropriate order, the transformations that must be applied to the base function f(x) to obtain the transformed function. Then, write the corresponding equation and transform the graph of f(x) to sketch the graph of g(x).

f(x) =\sqrt{x}, g(x) = 3f(x+ 6)

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Q13a

Describe, in the appropriate order, the transformations that must be applied to the base function f(x) to obtain the transformed function. Then, write the corresponding equation and transform the graph of f(x) to sketch the graph of g(x).

f(x) =x, g(x) = -f(6x)-5

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Q13b

Describe, in the appropriate order, the transformations that must be applied to the base function f(x) to obtain the transformed function. Then, write the corresponding equation and transform the graph of f(x) to sketch the graph of g(x).

f(x)= \frac{1}{x}, g(x) = \frac{1}{5}f(x) + 4

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Q13c

Describe, in the appropriate order, the transformations that must be applied to the base function f(x) to obtain the transformed function. Then, write the corresponding equation and transform the graph of f(x) to sketch the graph of g(x).

f(x)=x^2, g(x) = -2f(3x + 12) - 6

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Q13d

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) =\frac{1}{x}.

Then, transform the graph of f(x) to sketch the graph of g(x).

g(x) = 2x + 9

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Q14a

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) =\frac{1}{x}.

Then, transform the graph of f(x) to sketch the graph of g(x).

g(x) = \frac{3}{x + 4}

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Q14b

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) =\frac{1}{x}.

Then, transform the graph of f(x) to sketch the graph of g(x).

g(x) = -4\sqrt{x} = 1

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Q14c

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) =\frac{1}{x}.

Then, transform the graph of f(x) to sketch the graph of g(x).

g(x) =(5x + 20)^2

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Q14d

For each function f(x):

  • i) determine f^{-1}(x)
  • ii) graph f(x) and its inverse.
  • ii) state whether or not f^{-1}(x) is a function.

f(x)= 7x -5

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Q15a

For each function f(x):

  • i) determine f^{-1}(x)
  • ii) graph f(x) and its inverse.
  • ii) state whether or not f^{-1}(x) is a function.

\displaystyle f(x) = 2x^2 + 9

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Q15b

For each function f(x):

  • i) determine f^{-1}(x)
  • ii) graph f(x) and its inverse.
  • ii) state whether or not f^{-1}(x) is a function.

\displaystyle f(x) = (x+ 4)^2 + 15

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Q15c

For each function f(x):

  • i) determine f^{-1}(x)
  • ii) graph f(x) and its inverse.
  • ii) state whether or not f^{-1}(x) is a function.

\displaystyle f(x) = 5x^2 + 20x -10

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Q15d

Iai works at an electronics store. She earns $600 a week, plus commission of 5% of her sales.

a) Write a function to describe Jai’s total weekly earnings as a function of her sales.

b) Determine the inverse of this function.

c) What does the inverse represent?

d) One week, Iai earned $775. Calculate her sales that week.

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Q16