Task Sets: Determine explicit or recursive expressions - Common Core Math - HS Functions

Concepts

Which statement best describes an explicit expression for a function?

A rule that defines $f(n)$ in terms of $f(n-1)$ plus an initial value

A formula that gives the output $f(x)$ directly in terms of the input $x$ , without needing prior values

A list of step-by-step instructions that compute the output for any input

A table of input-output pairs that represents the function

A student writes the recursive rule $f(n) = f(n-1) + 4$ without providing
any other information.

Explain in one or two sentences why this definition is incomplete and what is
missing.

A phone plan charges $\text{\char"0024}30$ for up to 2 GB of data, then $\text{\char"0024}10$ for each
additional gigabyte, plus $\text{\char"0024}0.05$ per text message. Which representation
fits this situation best?

An explicit formula with a single expression

A recursive process using the previous month's bill

A procedural description — a series of calculation steps

A table of values listing all possible bills

Procedures

A plumber charges a flat fee of $\text{\char"0024}75$ plus $\text{\char"0024}40$ per hour. Which explicit
expression gives the total cost $C(h)$ for $h$ hours?

$C(h) = 75h + 40$

$C(h) = 40h + 75$

$C(h) = 40h$

$C(h) = 75 \cdot 40^h$

A recursive sequence is defined by $f(0) = 3$ and $f(n) = f(n-1) + 5$ .

What is $f(4)$ ?

A recursive sequence is defined by $f(0) = 4$ and $f(n) = f(n-1) \cdot 3$ .

A student computes $f(3) = 3 \cdot 3 = 9$ .

What error did the student make?

The student used the wrong initial value.

The student multiplied the input $n = 3$ by the multiplier, instead of
multiplying the previous output $f(2)$ by the multiplier.

The student should have added 3 instead of multiplying by 3.

There is no error; $f(3) = 9$ is correct.

The explicit formula for a linear sequence is $f(n) = 5n + 2$ .

In the recursive form $f(0) = a$ and $f(n) = f(n-1) + d$ ,
what is the value of $d$ (the common difference)?

An exponential function has the recursive definition $g(0) = 200$ and
$g(n) = g(n-1) \cdot 1.08$ .

What is the value of $g(0)$ in the equivalent explicit formula
$g(n) = A \cdot r^n$ ?

HSF.BF.A.1.a Tutor Intake — Explicit, Recursive, and Procedural Representations

Concepts

Procedures