Rational Functions Quiz

State the equation of the rational function that this graph represents.

• y = -2x + 1 / x - 3

• y = 2x + 1 / x - 3

• y = -2x + 1 / x+ 3

• y = 2x + 1 / x + 3

State the range of f(x) = 1 / 3x + 4.

• {y ∈ R | y > -4/3}

• {y ∈ R | y ≠ -4/3}

• {y ∈ R | y > 0}

• {y ∈ R | y ≠ 0}

The graph of which of the following rational functions has a hole?

• y = 2x - 6 / x - 6

• y = 2x - 3 / x - 3

• y = 2x - 6 / 2x

• y = 2x - 6 / x - 3

Identify the vertical and horizontal asymptotes of f(x) = x - 4 / 2x + 1.

• vertical: x = 4, horizontal: y = -1/2

• vertical: x = 4, horizontal: y = 1/2

• vertical: x = -1/2, horizontal: y = 1/2

• vertical: x = 1/2, horizontal: y = -1/2

Solve for x in (frac{x-2}{x} = frac{x-4}{x-6}).

• x = 3

• x = 4

• x = 6

• x = 8

• (-∞, -7] ∪ (2, ∞)

• (-∞, -7] ∪ (2, 7]

• (-∞, -7) ∪ (2, 7)

The senior girls basketball team is selling pizza slices at lunch to raise money for their trip to OFSAA. They spend $600 on boxes of pizza that have 8 slices each in them. They keep 4 pizzas to eat for themselves and sell the rest which makes them $1232 which is a profit of $1.50 per slice. How many slices did they sell?

• 400

• 432

• 472

• 500

The senior girls basketball team is selling pizza slices at lunch to raise money for their trip to OFSAA. They spend $600 on boxes of pizza that have 8 slices each in them. They keep 4 pizzas to eat for themselves and sell the rest which makes them $1232 which is a profit of $1.50 per slice. How much were they charging per slice?

• $2.00 per slice

• $2.75 per slice

• $3.00 per slice

• $3.50 per slice

Which of the following is a reciprocal function that has a vertical asymptote at x = 2, a horizontal asymptote at y = -3, and a hole at x = -1?

• f(x) = -3 + 1/(x-2)

• f(x) = (-3 x+ 1)(x+1)/(x-2)(x+1)

• f(x) = -3 + 1/(x+1)

• f(x) = -3 + (x-2)/(x+1)

When a saw is used to cut wood, a certain percent is lost as sawdust, depending on the thickness of the saw-blade. The wood lost is called the kerf. The percent lost, P(t) , can be modeled by the function P(t) = frac{100t}{t + W} , where t is the thickness of the blade and W is the thickness of the wood, both in millimeters. Consider a saw cutting a 30mm thick piece of wood. What is the significance of the horizontal asymptote?

• The horizontal asymptote represents the maximum percent of wood that can be lost as sawdust.

• The horizontal asymptote indicates the minimum thickness of the saw-blade required.

• The horizontal asymptote shows the maximum thickness of wood that can be cut.

• The horizontal asymptote is irrelevant in this context.