Lesson 2 You-Mix Cubes Solidify Understanding

Ready

Use the graph to write the equation of the quadratic function.

1.

2.

3.

4.

5.

6.

7.

What are the $y$ -intercepts for the graphs in problems 1–6?

8.

In problems 1 and 2, the $y$ -intercept is just the product of the $x$ -intercepts. Why isn’t that the case for problems 3, 4, 5, and 6?

Set

9.

Complete the tables for $f (x) = x$ and $g (x) = x^{3}$ and $h (x) = x^{5}$ .

a.

$x$	$f (x) = x$
$- 1$
$0$
$1$

b.

$x$	$g (x) = x^{3}$
$- 1$
$0$
$1$

c.

$x$	$h (x) = x^{5}$
$- 1$
$0$
$1$

10.

What does it mean when $f (x) = g (x) = h (x)$ ?

11.

Use the grid to graph $f (x) = x$ , $g (x) = x^{3}$ , and $h (x) = x^{5}$ on the interval $[- 1, 1]$ .

Fill in the blanks with $f (x)$ , $g (x)$ , and $h (x)$ to make a true statement.

12.

On the interval $(0, 1)$ , $<$ $<$ .

13.

On the interval $(1, \infty)$ , $<$ $<$ .

14.

Use the grid to graph $f (x) = x$ , $g (x) = x^{3}$ , and $h (x) = x^{5}$ on the interval $[- 2, 2]$ . (Some values will go off the grid.)

Go

Use the properties of exponents to multiply.

15.

$x^{\frac{1}{3}} \cdot x^{\frac{1}{6}} \cdot x^{\frac{1}{4}}$

16.

$a^{\frac{2}{5}} \cdot a^{\frac{3}{10}} \cdot a^{\frac{2}{15}}$

17.

$m^{\frac{4}{7}} \cdot m^{\frac{3}{14}} \cdot m^{\frac{5}{28}}$

Use the power to a power rule to rewrite each expression. (Answers will not have an exponent.)

18.

${(8^{\frac{1}{3}})}^{6}$

19.

${(10^{\frac{2}{5}})}^{10}$

20.

${(9^{\frac{1}{4}})}^{6}$

Show the work that justifies that the expressions are equivalent.

21.

$4 {(\frac{1}{2})}^{6} = {(\frac{1}{2})}^{4}$

22.

$15 {(\frac{2}{5})}^{3} = 6 (\frac{4}{25})$

23.

$54 \cdot {(\frac{2}{3})}^{5} = \frac{2^{6}}{3^{2}}$