Notes
What makes a function
A function gives exactly one output for each input. Check tables and ordered pairs for repeated inputs, and graphs with the vertical line test. The domain is the set of inputs and the range is the set of outputs.
Function notation
$f(a)$ is the output when the input is $a$. To evaluate, substitute. To find the input that gives a certain output, set $f(x)$ equal to that output and solve. $f(a) = b$ means $(a, b)$ is on the graph.
Reading graphs
Look for intercepts, where the graph increases or decreases, and maximums and minimums. In real situations, explain each feature with units.
Arithmetic sequences
Each term adds a common difference $d$: $a_n = a_1 + (n - 1)d$. They are linear functions on the counting numbers.
Topics in this unit
Each topic has its own short notes and practice.
Practice
Input 2 has two different outputs.
$-2(-3) + 9 = 6 + 9 = 15$.
$5x = 25$.
Input is miles, output is cost.
$2 + 24(4) = 98$.
The outputs are 4, 1, 0, 1, 4. List each once.
Free response
Write your answer first, then open the scoring guide.
Free-response question
A savings account starts with $80 and the owner adds $15 every week.
(a) Write a function $B(w)$ for the balance after $w$ weeks.
Show the answer and scoring guide
$B(w) = 80 + 15w$
Check off the points you earned:
(b) Find $B(12)$ and explain what it means.
Show the answer and scoring guide
$B(12) = 80 + 180 = 260$. After 12 weeks the balance is $260.
Check off the points you earned:
(c) After how many weeks will the balance first be at least $400?
Show the answer and scoring guide
$80 + 15w \ge 400 \Rightarrow 15w \ge 320 \Rightarrow w \ge 21.3$, so after 22 weeks.
Check off the points you earned: