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)

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)

Simplify each expression and state all restrictions on x.

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

Simplify each expression and state all restrictions on x.

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

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.

Simplify the expression and state the restrictions.

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

Simplify the expression and state the restrictions.

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

Simplify the expression and state the restrictions.

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

Simplify the expression and state the restrictions.

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

Simplify the expression and state the restrictions.

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

Simplify the expression and state the restrictions.

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

Simplify the expression and state the restrictions.

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

Simplify the expression and state the restrictions.

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

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?

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

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)

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

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

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

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

g(x) = f(-x)

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

g(x) = -f(x)

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

g(x) = -f(-x)

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

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

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)

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)

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})

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)

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

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}

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

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}

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)

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

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

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

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

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}

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

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

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

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

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

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

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.