same inverse variation., then c equals:
Test 2: Inverse functions, quadratic relations, and transformations
MQ6 home Test 1 Quadratic Relations Inverse Variations Test 3
MQ6 TEST 2A (answers below)
Mr.
Gary Jaye
INSTRUCTIONS: 1. Express all answers in simplest form , SHOW ALL
WORK, and box answers.
2. NO graphing CALCULATORS. 3. Use pen.
| 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 standard equation of the circle with the given center and radius. | |||
| d. C(h, k), radius r | e. C(0, 0), radius r | ||
| f. The standard formula for the distance between (x1, y1) and (x2, y2) is: | |||
| g. By subjecting the graph of a relation to the ________________________________________ , one can determine whether or not the inverse of a relation is a function. | |||
| 2. In a-j, fill in all the answers. [5, 4, 3, 3 off for first four wrong answers] | |
| a. ry-axis(x, y) = | g. R180° (x, y) = |
| b. rx-axis(x, y) = | h. R270° (x, y) = |
| c. ry=- x(x, y) = | i. Ta,b (x, y) = |
| d. ry=x(x, y) = | j. Dk(x, y) = |
| e. R(x, y) = | k. A direct isometry preserves: |
| f. R90° (x, y) = | l. An isometry which is not direct is a(n): |
| 3. In a-c, state whether or not the inverse of the relation represented by the graph is a function. (Y or N) [3, 1 for first two wrong answers] | ||
| a. Y or N:
|
b. Y or N:
|
c. Y or N:
|
| d. f and g are inverses when _____________ = ______________ [3] (More than one answer is acceptable.) | ||
| e. If (4, - 3) and (c,
6) belong to the
[3] same inverse variation., then c equals: |
||
| 4. In a-c, fill in the transformation that maps the graph defined by the first equation onto the graph defined by the second equation. [3, 3 for first two wrong answers] | ||
pre-image |
à transformation à |
image |
| a. y = x2 | y = - x2 | |
| b. y = x2 | y + 7 = (x - 4)2 | |
| c. y = sin x | x = sin y | |
In 5- 8, SHOW WORK and box answers
| 5. Given f(x) = 1/(2x + 3); find f- 1(x). The variable y should not appear in your final answer. [7] |
|
|
| 6. Given {(x, y): x = - y2 + 4y - 5}. [15] | |
| a. Transform algebraically.
|
b. Make rough sketch, label vertex.
|
| vertex: | number of x-intercepts: |
| domain: | number of y-intercepts: |
| range: | |
| 7. Given x2 + y2 - 6x + 10y = - 30; a. Transform algebraically, b. Make rough sketch, and answer accompanying questions. [18] | |
| a. Transform algebraically.
|
b.
|
| center: | number of x-intercepts: |
| radius: | number of y-intercepts: |
| domain: | equation of one line of symmetry: |
| range: | coordinates of point of symmetry: |
| 8. Given {(x, y): y = - 2/x} Use scrap area below as needed to (a) Make rough sketch and answer accompanying questions: [15] | |
| scrap area
|
a.
|
| domain: | number of y-intercepts: |
| range: | equation of one line of symmetry: |
| number of x-intercepts: | coordinates of point of symmetry: |
| With respect to this graph, the x- and y-axes are: | |
ANSWERS: 1a-1c. See Test 1
2a. (-x,y) 2b. (x,-y)
2c. (-y,-x)
2d. (y,x) 2e. (-x,-y)
2f. (-y,x) 2g. (-x,-y)
2h. (y,-x) 2i. (x+a,y+b) 2j. (kx, ky)
2k. orientation 2l. line reflection 3a. Y
3b. N 3c. Y
3d. (f ° g)(x) = (g ° f)(x) ,
Other answers are acceptable. 3e. c = -2
4a. rx-axis or R180°
4b. T4,- 7
4c. ry=x 5. f- 1(x) = (1- 3x)/2x 6a. x+1 = -(y2- 2)2, V(-1,2), D = {x £ -1}, range = {y Î
R}, one x-intercept,
0 y-intercepts. 7a. (x- 3)2 + (y+5)2
= 22, C(3,-5), radius = 2, D = {1 £ x £
5}, R = {-7 £ y £ -3},
zero x- and y-intercepts, eqtns of 2 lines of symmetry: x = 3 and y = -5, point of symmetry: (3, -5)
8. D = {x ¹ 0}, R = {y ¹ 0}, zero
x- and y-intercepts, eqtns of lines of symmerty: y = x, y = -x,
point of symmetry: (0,0), x- and y-axes are asymptotes.
MQ6 home Test 1
Quadratic Relations Inverse
Variations Test 3
