Function Notation: Reading f(x) and Functions in Tables

Work each one out before you check it. Every question has a scratch pad and a calculator.

1. Question 1

   The function $P = f(t)$ gives a town's population, in thousands, $t$ years after 2000. In 2015 the town had 48,000 people. Write this fact as $f(a) = b$.

   $a =$

   $b =$

   Check

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2. Question 2

   The function $x = g(y)$ gives the length $x$, in centimetres, of a plant $y$ weeks after it was planted. You are told $g(6) = 45$. How many days after planting is this, and how long is the plant then, in metres?

   days after planting:

   length in metres:

   Check

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3. Question 3

   The function $f$ is given by the table

   $$\begin{array}{c|cccccc} x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline f(x) & 5 & -2 & 4 & 0 & 3 & 1 \end{array}$$

   Find $f(1 + 3)$.

   $f(1+3) =$

   Check

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4. Question 4

   Each table pairs inputs $x$ with outputs $y$:

   $$\text{A: }\begin{array}{c|ccc} x & 1 & 2 & 3 \\ \hline y & 4 & 4 & 4 \end{array}\qquad \text{B: }\begin{array}{c|ccc} x & 0 & 3 & 0 \\ \hline y & 5 & 2 & 5 \end{array}$$

   $$\text{C: }\begin{array}{c|ccc} x & -1 & 2 & -1 \\ \hline y & 0 & 6 & 7 \end{array}\qquad \text{D: }\begin{array}{c|ccc} x & 2 & 3 & 4 \\ \hline y & 1 & -1 & 1 \end{array}$$

   How many of the four tables represent $y$ as a function of $x$?

   Check

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5. Question 5

   A function is written $Q = g(n)$. Its values are given in a table that lists the $Q$ row first:

   $$\begin{array}{c|cccc} Q & 5 & 0 & 5 & -3 \\ \hline n & 1 & 2 & 3 & 4 \end{array}$$

   Which list writes the table in function notation?

   a

   $g(5) = 1,\ g(0) = 2,\ g(5) = 3,\ g(-3) = 4$

   b

   $Q(1) = 5,\ Q(2) = 0,\ Q(3) = 5,\ Q(4) = -3$

   c

   $g(1) = 0,\ g(2) = 5,\ g(3) = -3,\ g(4) = 5$

   d

   $g(1) = 5,\ g(2) = 0,\ g(3) = 5,\ g(4) = -3$

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