Answers
To Sample Test
1) Domain -- x < 4
Range -- y >
0
Zero at ( 4, 0)
2) Domain -- all real numbers but 2/3
Range -- all real numbers
but 5/3
Zero at ( 0, 0)
3) Range is all real numbers
zeros at (-4, 0), (-1, 0),
and (1, 0)
4) a) 5x + 5
b) -2x
c) 4(x + 5)2
d) (2x + 5)2
e) 4/x, x can't equal
0
f) g[f(7)] = g(28)
= 784
5)
a)
b)
c)
6)
|
x |
y |
y = x |
origin |
| a) |
no |
no |
no |
yes |
| b) |
yes |
yes |
no |
yes |
| c) |
no |
yes |
no |
no |
7) It is symmetric to the x-axis
8) a) is a vertical stretch and translation
of 1 right and 5 up
b) is a reflection
about the x-axis and a translation of 1 left and 3 down
9) To prove this you must show
both ways!!
f[g(x)] = f(2x-1) = (2x - 1 +
1)/2 = 2x/2 = x
g[f(x)] = g[(x + 1)/2] = [2(x
+ 1)/2] - 1 = x + 1 - 1 = x
10) To find the rule interchange x and y and
solve for y.
x = y2 - 2
x + 2 = y2
_____
y = - \/ x + 2 , x > -2
11)
a)
b)
12) a) A(b, h) = bh/2
b)
A(2, 3) = (2)(3)/2 = 3 and A(5, 6) = (5)(6)/2 = 15
c)
5 = bh/2 ==> 10 = bh ==> h = 10/b
13) a) 4
b) 1, 0, -1, 0
c) -1, 1, 0, 1
d) Changes amplitude
but not period length.
e) Changes period
length to 2 (horizontal shrink) but does not change amplitude
f) Reflection
about the x-axis
g) Reflection
about the y-axis
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Hope
you did well on this opportunity. If not go back and study the previous
sections until you have mastered the material. Especially study the
reflections, stretches and shrinks, and of course, the translations.
Good luck!!
