Lesson 2 You-Mix Cubes Solidify Understanding

Ready

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

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

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?

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

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

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.

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

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

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.)

Use the properties of exponents to multiply.

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

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

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

Write the conjugate of each complex number.

$- 5 + 2 i$

$23 - 89 i$

$- 4 - 17 i$