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

Warm-Up: Review What You Know

If $f(x) = 3x - 1$ , what is $f(4)$ ?

A sequence is defined as a function with what type of domain?

All real numbers

Positive real numbers

Integer domain (counting numbers)

Rational numbers only

The sequence $a_n$ has $a_1 = 10$ and each term is 4 less than the previous. What is $a_3$ ?

Fluency Practice

A parking garage charges $5 to enter plus $3 per hour. The explicit formula for the total cost is $C(h) = 3h + 5$ . Find $C(7)$ .

A bank account starts with $2000 and grows by 4% per year. The explicit formula is $V(t) = 2000(1.04)^t$ . Find $V(3)$ . Round to the nearest cent.

A sequence starts at $f(0) = 6$ . Each term is 5 more than the previous. Which is a correct recursive definition?

$f(0) = 6$ , $f(n) = f(n-1) + 5$

$f(n) = f(n-1) + 5$ (no initial value stated)

$f(0) = 6$ , $f(n) = 5n$

$f(0) = 6$ , $f(n) = f(n) + 5$

A recursive sequence is defined by $f(0) = 3$ and $f(n) = f(n-1) \cdot 2$ . What is $f(4)$ ?

The explicit formula $f(n) = 4n + 7$ corresponds to a recursive definition with $f(0) = 7$ . What value is added at each step (the common difference)?

Exercises: Determine Explicit, Recursive, or Procedural Representations

Warm-Up: Review What You Know

Fluency Practice