Question

Solving problems with linear systems

Answer 1

didn't we solve this yesterday? we got 25

Answer 2

yeah idk y they asked it again,,,

Answer 3

we also solved this yesterday

Answer 4

budget is less than/equal to 65,000

more expensive tree >= less expensive tree

Answer 5

*56,000

Answer 6

when you see (x+h) in the transformation, you get shifted left h units

so f(x+2) is the graph of x^2 shifted left 2 units

Answer 7

do u need to see the graphs?

Answer 8

not really,

again, since we have f(x+1) we shift the graph of f(x) = x^3 to the left 1 unit

Answer 9

would we go to the left 3?

Answer 10

yes

Answer 11

if you see f(x-h) it gets moved to the right h units

so f(x-4) is f(x) moved to the right 4 units

Answer 12

the +2 is outside the parentheses so we move the function up 2 units

Answer 13

the -5 is outside the parentheses so we move down 5 units

Answer 14

the (1/4) is inside the parentheses so the function gets "squished" (let me try sketching)

Answer 15

same thing, the function gets "flatter"

Answer 16

function gets "stretched" so the slope becomes steeper

Answer 17

since the stretch factor is less than 1 the graph becomes less steep

Answer 18

stretch factor is >1 so graph becomes steeper

Answer 19

does it show you the graph of f(x)?

Answer 20

no not this one

Answer 21

since it gets shifted to the right 1 unit I guess I would add 1 to the x-value to get (2,5)? hm.

Answer 22

add 4 to the x-value to get (2,-1)

Answer 23

subtract 2 from the x-coordinate

Answer 24

so (0,9)?

Answer 25

good

Answer 26

add 4 to the y-coordinate

Answer 27

5,8?

Answer 28

good

Answer 29

subtract 4 from the y-coordinate

Answer 30

2,-1

Answer 31

good

Answer 32

hm. I ~believe~ you would multiply the x-coordinate by (3/4)

Answer 33

so -4 1/2,-5

Answer 34

I think so :S

Answer 35

multiply x-coordinate by (-2/3)

Answer 36

ok so the little circle thing means we put f(x) as x into equation g(x)

Answer 37

g(x) = x^2 = (-x-2)^2

if x = - 6, then (-x-2)^2 = ?

Answer 38

40?

Answer 39

do the parentheses first

if x = -6, then -x - 2 = ?

Answer 40

4?

Answer 41

good, and 4^2 = ?

Answer 42

16

Answer 43

good so 16 = your ans

Answer 44

similar as before

f(x) = 2x + 6
g(x) = x^3

g(x) dot f(x) = (2x+6)^3, and if x = 0, then this equals...?

Answer 45

216?

Answer 46

again, parentheses first

if x = 0, 2x + 6 = ?

Answer 47

6

Answer 48

?

Answer 49

good

and 6^3 = ?

Answer 50

216

Answer 51

oh you were right the first time, it's 216 >>

Answer 52

as your answer

Answer 53

same thing

g dot f(x) = (7x+8)^4
x = 0

ans = ?

Answer 54

4096?

Answer 55

good

Answer 56

f(x) = -x+ 7
g(x) = square root(x-3)

f dot g(x) = -square root(x-3) + 7
x = 4

ans = ?

Answer 57

-9.6?

Answer 58

not quite

start with the parentheses

if x = 4, then x - 3 = 1

square root of 1 = 1
-square root of 1 = -1

(- square root of 1) + 7 = 6 = your answer

Answer 59

if g(x) = sqare root(x+1) and x = 24, what is g(x)?

Answer 60

um... idk

Answer 61

how do i square root x?

Answer 62

start with the parentheses first

if x = 24, then x + 1 = 25

what's the square root of 25?

Answer 63

5

Answer 64

so the answer would be 5?

Answer 65

not yet

Answer 66

now we plug that into f(x)

if x = 5, then f(x) = -9x + 9 = ?

Answer 67

so -36 is the answer?

Answer 68

good, yes

Answer 69

same thing as before

x = 7
g(x) = square root(x-6)

g(x) = ?

Answer 70

1

Answer 71

good, now we re-substitute back into f(x)

x = 1
f(x) = -5x - 1 = ?

Answer 72

-6

Answer 73

good, that's your ans

Answer 74

f dot g = (-9x+3)^4 = ans

Answer 75

can we open a new question after this

Answer 76

yeah

Answer 77

is -6554 right?

Answer 78

no, it's asking for a function, not a number

Answer 79

(-9x+3)^4 = answer

Answer 80

oh lol