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Mathematics Functions and Financial Planning

Group 1

Use the vertical line test to determine which of the following relations are functions:
Graphs for vertical line test

Question 1a

Short answer
Graph a

Question 1b

Short answer
Graph b

Question 1c

Short answer
Graph c

Question 1d

Short answer
Graph d

Question 1e

Short answer
Graph e

Question 1f

Short answer
Graph f

Question 1g

Short answer
Graph g

Question 1h

Short answer
Graph h

Group 2

If \( f(x) = 3x - x^2 + 2 \), find the value of:

Question 2a

Short answer
f(0)

Question 2b

Short answer
f(3)

Question 2c

Short answer
f(-3)

Question 2d

Short answer
f(-7)

Question 2e

Short answer
f(\frac{3}{2})

Group 3

For a hot air balloon ride, the function \( H(t) \) gives the height of the balloon after \( t \) minutes. Its graph is shown alongside.
Graph of H(t) showing height of the balloon over time

Question 3a

Short answer
Find \( H(30) \), and explain what your answer means.

Question 3b

Short answer
Find the values of \( t \) such that \( H(t) = 600 \). Interpret your answer.

Question 3c

Short answer
For what values of \( t \) was the height of the balloon recorded?

Question 3d

Short answer
What range of heights was recorded for the balloon?

Group 4

Heather has just retired at age 65. She has $900,000 in her savings fund. She “rolls over” the money into an annuity fund which returns 4% p.a. compounded monthly.

Question 4a

Short answer
If Heather withdraws $5400 per month to live on, how long will it take for the money in the fund to run out?

Question 4b

Short answer
If Heather wants the money to last until she is 90 years old, how much can she afford to withdraw each month?

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