Test 4: Exponential and logarithmic relations and their graphs

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MQ6 TEST 4A  (answers below)                                                                                      Mr. Gary Jaye

INSTRUCTIONS:   1. Express all answers in simplest form and SHOW   WORK when requested.
                                2. NO  CALCULATORS.  3. Use pen and label all graphs and axes..

1. In a - g, fill in all the answers. [5, 4, 3 off for first 3 wrong answers]
In #a- c, fill in the three Pythagorean identities.
a.	b.			c.
In d- e, state the two standard equations of the unit circle, center at origin.
d.		e.
f. In simplest form, the equivalent expression for is:
g. The transformation that maps the graph of y = bx onto the graph of y = (1/b)x is:			h. When the graph of y = bx is reflected over the line defined by y = x, the equation of the image is y = _________________ . (Answer must be in y = ??? form.)

2. Express in simplest radical form. (show work). [a-g are 3 each]
a.
b.	c.
d.	e.
f.	g.
h. Express as a single radical in simplest form. [5]

3. Evaluate and express angles in RADIAN measure. [a- d are 3 each]
a. sin[Tan-1(- 1)]	b.
c. sin[Sin-1(2/7)]	d. Cos-1[cos(4p /3)]
e. tan[Sin-1(3/4)] SHOW WORK. [6]

4. Evaluate the expression. [3 each]
a. 813/4	b.
c.	d.

6a. Sketch graph of y = 2x and its image under a reflection in line defined by y = x. [14 for #6]
b. equation of the image:	c. range of the equation of the     image:	d. significant feature of image:

8a. Sketch graph of y = sin-1x over - p £ y £ 2p . [15 for #8]
8b. Draw box around portion of graph of y = sin-1x that represents the graph of y = Sin-1x.
8c. Fill in domain and range of y = sin-1x domain: range:	8d. Fill in domain and range of y = Sin-1x domain: range:

ANSWERS:  1a-1c. sin² q + cos²q = 1, tan²q + 1 = sec²q , and cot²q + 1 = csc²q     1d-1e.  x² + y² = 1,
sin²q + cos²q = 1    1f. 1   1g.   r_y-axis    1h. y = log_bx    2a.    2b.     2c. a^p     2d.
2e.    2f.    2g. Ö (5)/5    2h.    3a. - Ö (2)/2   3b. - Ö (3)/3   3c. 2/7    3d. 2p /3, not 4p /3
e.    4a. 27   4b. 81/16    4c. - 3   4d. 4/3   5a. x = 2    5b. x = 3   6b. y = log₂x 6c. y-axis is a vertical asymptote
7a. 0 £ Cos- ¹x £ p   7b. - p /2 < Tan- ¹x < p /2   8c. domain = {x: - 1 £ x £ 1}, range = R
8d. domain = {x: - 1 £ x £ 1}, range = {y: - p /2 £ y £ p /2}

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