Task Sets: Graph root and piecewise functions - Common Core Math - HS Functions

Concepts

Which statement correctly describes the domain and range of the parent
function $f(x) = \sqrt{x}$ ?

Domain: all real numbers; Range: all real numbers

Domain: $x \geq 0$ ; Range: $y \geq 0$

Domain: $x \geq 0$ ; Range: all real numbers

Domain: all real numbers; Range: $y \geq 0$

Evaluate $g(-8)$ for the cube root function $g(x) = \sqrt[3]{x}$ .
(Enter a single integer.)

A piecewise function is defined as:

$f(x) = \begin{cases} x + 1 & \text{if } x < 3 \\ 7 & \text{if } x \geq 3 \end{cases}$

At $x = 3$ , the graph should show:

A solid dot at $(3,\,4)$ and an open circle at $(3,\,7)$ .

An open circle at $(3,\,4)$ and a solid dot at $(3,\,7)$ .

Solid dots at both $(3,\,4)$ and $(3,\,7)$ .

Open circles at both $(3,\,4)$ and $(3,\,7)$ .

For the transformed square root function $f(x) = 2\sqrt{x - 3} - 1$ ,
what is the $y$ -value when $x = 7$ ?

For the transformed square root function $f(x) = 2\sqrt{x - 3} - 1$ ,
what is the smallest value in the domain? (Enter a single number.)

Evaluate the piecewise function at $x = 2$ :

$g(x) = \begin{cases} 2x & \text{if } x \leq 3 \\ x + 3 & \text{if } x > 3 \end{cases}$

What is $g(2)$ ?

For the piecewise function:

$g(x) = \begin{cases} 2x & \text{if } x \leq 3 \\ x + 3 & \text{if } x > 3 \end{cases}$

Evaluate both pieces at $x = 3$ . Enter the output value that the
first piece (the piece that applies at $x = 3$ ) gives.

The absolute value function $f(x) = |x|$ is graphed correctly as:

A U-shaped curve (smooth parabola) with vertex at the origin.

A V-shape with a sharp corner at the origin and slopes $+1$ and $-1$ .

A V-shape with a sharp corner at the origin and slopes $+2$ and $-2$ .

A horizontal line at $y = 0$ .