Relations and Functions: math test, Grade 9 – download the PDF

1 Relations / 4 pts

Let \(S = \{(0, 6), (1, 4), (2, 6), (5, -3)\}\).

1. Give the domain and the range of \(S\).
2. Is \(S\) a function? Explain.
3. Which inputs have the output \(6\)?
4. Change one pair so that \(S\) is no longer a function.

2 Function notation / 4 pts

Let \(f(x) = -2x + 9\). Find (a) \(f(3)\), (b) \(f(-4)\), (c) \(x\) such that \(f(x) = 1\), (d) \(x\) such that \(f(x) = -5\).

3 Reading a graph / 4 pts

The graph shows a function \(h\) for \(-1 \le x \le 5\), where \(h(x) = -x^2 + 4x\).

1. Read \(h(2)\).
2. Find the \(x\)-values where \(h(x) = 0\).
3. Find the \(x\)-values where \(h(x) = 3\).
4. Give the range of \(h\) for \(-1 \le x \le 5\).

4 Table and rule / 3 pts

A linear function \(f\) is given by this table.

1. Give the domain and the range of the table.
2. Find the rule \(f(x)\).
3. Compute \(f(15)\).

5 Arithmetic sequence / 3 pts

Consider the sequence \(11, 8, 5, \dots\), which is arithmetic.

1. Find the common difference and the rule \(a_n\).
2. Find \(a_9\).
3. Find the first negative term.

6 Gym membership / 2 pts

A gym charges a 25-dollar sign-up fee plus 12 dollars per month. Calculator allowed.

1. Write the cost function \(C(m)\) and find \(C(8)\).
2. With a budget of 200 dollars, what is the greatest number of whole months you can afford?