Lesson 4 Root Knowledge Practice Understanding

Ready

Max and Ace often ride their bikes to school, which is $4 miles$ from their home. Write answers in mph.

1.

Write a function that describes the relationship between speed and time.

2.

What is their average speed if it usually takes $30 minutes$ to get to school?

3.

One day, it was raining, and it only took $15 minutes$ to get to school. What was their average speed?

4.

On the way home from school, Max and Ace like to play a game called “the best found thing.” In order to win the game, you need to find something cool. So, they go slowly and watch for things on the ground and under shrubs. When they play this game, the ride home usually takes $2 hours$ . What is their average speed on these days?

5.

What would their average speed need to be if they planned to take $1 hour$ and $15 minutes$ to get to school?

6.

Use the values you derived in problems 1–4 to fill in the table, showing the time it takes to get to school based on the speed Max and Ace want to go.

$t (hours)$	$\frac{1}{4} hour$
$s (mph)$

7.

Complete the sentence.

Speed ( $s$ ) varies with elapsed time ( $t$ ).

Set

Use technology to graph each function. Then state the domain.

8.

$y = \sqrt{2 x - 10}$

9.

$y = \sqrt{- 6 x}$

10.

$y = \sqrt{4 (x + 3)}$

11.

$y = \sqrt{3 (x - 5)} + 1$

12.

$y = \sqrt{9 x}$

13.

$y = \sqrt{- x}$

Solve each square root equation. Check your solution.

14.

$\sqrt{x} = 4$

15.

$\sqrt{x} + 4 = 20$

16.

$\sqrt{5 x - 7} = 2$

17.

$- 4 \sqrt{4 x - 3} = - 12$

18.

$- 5 = 3 \sqrt{x}$

19.

$2 \sqrt{5 x + 2} = 24$

Identify the following functions as either exponential, quadratic, or square root. Identify at least three unique features for each graph that helped you identify it.

20.

21.

22.

23.

The three graphs in problems 20–22 share the point $(4, 16)$ . Write the equation that defines each graph.

Go

Find the length of the pre-image and the image. Name the type of transformation. Indicate whether the transformation preserved distance or did not preserve distance.

24.

Segment $A B$ defined by $A (- 6, 13) B (4, - 2)$

Segment $A^{'} B^{'}$ where $A^{'} (x, y) \to (x + 6, y - 3)$ and $B^{'} (x, y) \to (x + 6, y - 3)$

25.

Segment $M N$ defined by $M (5, 22) N (3, 4)$

Segment $M^{'} N^{'}$ where $M^{'} (x, y) \to (x - 10, y - 4)$ and $N^{'} (x, y) \to (x - 10, y - 4)$

26.

Segment $R D$ defined by $R (- 10, 13) D (- 2, - 2)$

Segment $R^{'} D^{'}$ where $M^{'} (x, y) \to (2 x, 2 y)$ and $N^{'} (x, y) \to (2 x, 2 y)$

27.

Segment $S T$ defined by $S (17, 11) T (20, 7)$

Segment $S^{'} T^{'}$ where $S^{'} (x, y) \to (- 6 x, - 6 y)$ and $T^{'} (x, y) \to (- 6 x, - 6 y)$