Lesson 2 Shift and Stretch Solidify Understanding

Ready

Find the zeros of each polynomial function.

1.

$p (x) = (x + 4) (x - 2) (x - 7)$

2.

$p (x) = (2 x - 6) (8 x - 1) (x - 5)$

3.

$p (x) = (9 x + 3) (x^{2} - 9)$

4.

$p (x) = x^{2} + 25$

Find the domain of each of the rational functions.

5.

$q (x) = \frac{1}{(x + 4) (x - 2) (x - 7)}$

6.

$q (x) = \frac{1}{(2 x - 6) (8 x - 1) (x - 5)}$

7.

$q (x) = \frac{1}{(9 x + 3) (x^{2} - 9)}$

8.

$q (x) = \frac{1}{x^{2} + 25}$

Set

Identify the vertical asymptote, horizontal asymptote, domain, and range of each function. Then sketch the graph on the grids provided.

9.

$f (x) = \frac{4}{x}$

vertical asymptote:

horizontal asymptote:

domain:

range:

10.

$f (x) = \frac{3}{x} + 2$

vertical asymptote:

horizontal asymptote:

domain:

range:

11.

$f (x) = - \frac{5}{x - 3}$

vertical asymptote:

horizontal asymptote:

domain:

range:

12.

$f (x) = \frac{1}{(x + 5)} - 4$

vertical asymptote:

horizontal asymptote:

domain:

range:

13.

Write a function of the form $f (x) = \frac{a}{x - h} + k$ with a vertical asymptote at $x = - 15$ and a horizontal asymptote at $y = - 6$ .

Go

Use the given root to find the remaining roots. Then write an equivalent form of the function.

14.

$f (x) = x^{3} - x^{2} - 17 x - 15$

Given root: $x = - 1$

15.

$f (x) = x^{3} - 3 x^{2} - 61 x + 63$

Given root: $x = 1$

16.

$f (x) = 6 x^{3} - 18 x^{2} - 60 x$

Given root: $x = 0$

17.

$f (x) = x^{3} - 14 x^{2} + 57 x - 72$

Given root: $x = 8$

18.

$f (x) = x^{3} - 5 x^{2} + 4 x - 20$

Given root: $x = 2 i$