Task Sets: Use function notation - Common Core Math - HS Functions

Warm-Up: Review What You Know

These problems review skills you have already learned.

A function $f$ is given by the table below.

$x$	$f(x)$
1	5
2	8
3	11
4	14

What is $f(3)$ ?

Let $f(x) = 3x - 4$ . Evaluate $f(5)$ .

The pool context: the number of swimmers $t$ hours after opening is $S(t)$ .
The statement " $S(3) = 85$ " means: "Three hours after opening, there are ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ swimmers."
In this context, the input $t = 3$ represents ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

number of swimmers:

what the input represents:

Fluency Practice

Evaluate each function as directed. Show your substitution steps.

Let $f(x) = x^2 - 3x + 2$ . Evaluate $f(-1)$ .

Let $g(t) = t^2 + 1$ . Evaluate $g\!\left(\dfrac{1}{2}\right)$ .

Express your answer as a fraction in simplest form or as a decimal.

Let $h(x) = \sqrt{x - 3}$ . Which of the following is undefined (not in the domain)?

$h(7)$

$h(3)$

$h(1)$

$h(12)$

$Table showing four substitution steps for f(x) = 2x + 3 with inputs 4, a, a+1, and x+h$

Let $f(x) = 2x + 3$ . Complete the table by filling in each output.

Input	Notation	Output
$x = 4$	$f(4)$	̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
$x = a$	$f(a)$	̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
$x = a+1$	$f(a+1)$	̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
$x = x+h$	$f(x+h)$	̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

f(4):

f(a):

f(a+1):

f(x+h):

Let $f(x) = x^2$ . Which statement is true when $a = 2$ and $b = 3$ ?

$f(a + b) = f(a) + f(b)$

$f(a + b) > f(a) + f(b)$

$f(a + b) < f(a) + f(b)$

$f(a + b) = f(a) \cdot f(b)$

Exercises: Use Function Notation

Warm-Up: Review What You Know

Fluency Practice