MHF4U0 Unit 5 Test: Rational Fn’s, Eq’s and Inequalities

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MHF4U0 Unit 5 Test: Rational Fn’s, Eq’s and Inequalities

Knowledge (16 marks)

1)  Match each function to its correct graph:

2) Solve. Leave your answers in exact simplified form:

3) Use an interval chart to find the solution:

4) Sketch the graph of

Application (14 marks):

5) The graph of a function y = f (x) is shown on the right. Sketch the graph of y =1/f (x) on the same axes.


6) Sarah purchased a shipment of calculators for $3082.50. She kept 15  calculators to give as Christmas presents for her closest friends and sold the remaining calculators for $3751.50, making a profit of $8.25 on each calculator that she sold. Determine the number of calculators in the original shipment.

7) The Research In Motion company estimates that the profit/ item functions for a BlackBerry is given by: P(x) = , where x is the

number of phones produced in thousands, and C is in dollars $.

a. How many phones must be produced for the Revenue of a BlackBerry to

be $150?

b. What will be the Marginal Revenue at a level of production of 5 000 phones?

Communication ( 9 marks)

8) Describe what happens to the value off(x) =

4x + 2

3x 一 5

as x-> 伪 .

9) Explain the difference between the solution to the equation = and the solution to the inequality > .

10) The graph on the left contains a hole where x = 3. Determine a possible equation for the graph.

Thinking ( 8 marks)

11) The Westfield Basketball Team bought pizza for $1200 to sell at the     game. They kept 30 pizzas to feed the players after the game and sold the rest for $2250. There were 14 slices in each pizza. Their profit was $2 a slice.

a) How many pizzas were in the original order?

b) What was the original price of each pizza?

c) What did they charge per slice?

12) Estimate the slope of the tangent line to the graph off (x) = 4x    at the point where x = 0 and find the average rate of change for the function over the interval [3, 4].


2023-07-19