Function Notation and Interpretation

You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 77 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Function Notation and Interpretation — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionDefining Piecewise and Step Functions IntroductoryAssessment Practice

3 marks~5 minCriterion C

A postal company charges for packages according to the step function shown in the graph below.

The cost (in dollars) remains constant within each weight interval and jumps at specific weight boundaries.

Explain what the open and closed circles at each boundary point on the graph indicate about which interval includes that boundary weight. [1]

Deduce the cost of posting a package weighing 3.5 kg. [1]

A customer has a budget of 9 dollars. Advise the customer whether this budget is sufficient to post a package weighing exactly 4 kg, and what weight limit they must stay within to achieve a lower cost. [1]

Solutions

2QuestionInterpreting Function Values in ContextAssessment Practice

4 marks~6 minCriterion A

The height

h

(in metres) of a ball thrown upward is modelled by a downward-opening parabola with vertex

(2,\ 20)

, intersecting the

t

-axis at

t = 0

s and

t = 4

s, where

t

is time in seconds.

Interpret the graph to describe how the height of the ball changes over the four-second flight. [1]

Deduce the equation of the parabola in the form

h(t) = a(t - p)^2 + q

, and hence calculate the height of the ball at

t = 1

s. [2]

A safety sensor triggers if the ball remains above

15

m for longer than

1.5

seconds. Justify whether the sensor is triggered during the flight. [1]

Solutions

3QuestionInterpreting Function Values in ContextAssessment Practice

8 marks~12 minCriterion D

A city council models the total cost (in dollars) of running a community recycling program for

t

months using

C(t) = 5000 + 120t

, where 5000 dollars represents the initial setup cost. The total benefit (in dollars) from reduced landfill fees is modelled by

B(t) = 2000\sqrt{t}

Calculate

C(12)

and

B(12)

. Interpret both results in the context of the recycling program. [2]

Justify whether the recycling program is financially worthwhile after 12 months. [2]

Advise the city council on whether these two functions are sufficient to support long-term financial decision-making. In your response, identify at least two assumptions made by each function and at least two limitations of the models overall. [4]

Solutions

4QuestionUnderstanding Function Notation f of xAssessment Practice

6 marks~9 minCriterion B

A biologist models the growth of a bacterial colony. The population (in thousands) at each hourly stage is defined by

a_1 = 2

and the recurrence relation

a_{n+1} = f(a_n)

, where

f(x) = 3x - 1

.

The first four hourly populations are:

a_1 = 2

a_2 = 5

a_3 = 14

a_4 = 41

Calculate

f(f(f(2)))

. [2]

Deduce a general formula for

a_n

in terms of

n

. [3]

The laboratory has capacity for 400 thousand bacteria. Using your formula from part (b), justify whether the laboratory capacity is exceeded at stage 6. [1]

Solutions

Questions 5-81

Unlock these questions with Premium

That's every free question here — 4 of 81.

+77 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade