HSF.IF.C.7.b: Graph root and piecewise functions — Practice

1

Which of the following is a strategic point for graphing $f(x) = \sqrt{x}$ ? (Choose the option where all three points lie on the graph.)

A.

$(0, 0)$ , $(1, 1)$ , $(4, 2)$

B.

$(0, 0)$ , $(2, 4)$ , $(3, 9)$

C.

$(-4, -2)$ , $(0, 0)$ , $(4, 2)$

D.

$(0, 0)$ , $(1, 2)$ , $(4, 4)$

2

Which statement correctly compares the parent functions $y = \sqrt{x}$ and $y = \sqrt[3]{x}$ ?

A.

Both have domain $[0, \infty)$ and range $[0, \infty)$ .

B.

$y = \sqrt{x}$ has domain $[0, \infty)$ ; $y = \sqrt[3]{x}$ has domain $(-\infty, \infty)$ .

C.

Both graphs pass through the origin but only $y = \sqrt{x}$ is always increasing.

D.

$y = \sqrt[3]{x}$ has domain $[0, \infty)$ and $y = \sqrt{x}$ has domain $(-\infty, \infty)$ .

3

Find three strategic points for $f(x) = 2\sqrt{x - 3} - 1$ and state the domain. (Hint: use inputs that make $x - 3$ a perfect square.)

4

Find three strategic points for $h(x) = \sqrt[3]{x + 1} - 2$ and state the domain.

5

Consider the piecewise function:
$f(x) = \begin{cases} x + 2 & \text{if } x < 1 \\ 4 & \text{if } x \geq 1 \end{cases}$
(a) Evaluate $f(0)$ , $f(1)$ , and $f(3)$ .
(b) Is the function continuous at $x = 1$ ? Explain.
(c) State the domain and range.

Exercises: Graph Square Root, Cube Root, and Piecewise-Defined Functions

Recall / Warm-Up

Fluency Practice