Question

For each function find f(-2), f(-0.5), and f(3).

7.f(x)= -x +4

Answer 1

so the function f is a function of the variable x , we write f(x), and say 'f of x'

when x is at the point -2 f of x is f(-2)


the value of the function f(x) = -x+4
at the point x=-2

is thus

f(-2) = -(-2)+4
= [ simplify this ]

Answer 2

How would I simplify that?

Answer 3

Would it be f(-2) =6?

Answer 4

do you understand what i have said?

to simplify

f(-2) = -(-2) +4


you have to use the fact that the negative of a negative becomes a positive

so -(-2) is equal to +2


f(-2) = -(-2) +4
= 2 +4
=

Answer 5

oh yeah i see you got 6 , thats right!

Answer 6

now

f(-0.5) is the same technique


sub x = (-0.5)
into
f(x) = -(x) +4

f(-0.5) = -(-0.5) +4
and simplify...
=

Answer 7

f(-0.5) =4.5?

Could you help me with this also

For each function to determine whether y varies directly with x. If so find the constant of variation and write the function.
x = -2, 1, 2
y = 3, 4 , 7
and I got 3/-2 = 4,1 = 7/2, but I don't understand, because y doesn't vary directly with x, but it doesn't seem finished.

Answer 8

f(-0.5) =4.5, yes!

Answer 9

for this next problem
you have these points
(x, y) = (-2,3), (1,4), (2,7)

right?

Answer 10

Yes

Answer 11

if you plot the points and try to draw a straight line through them , what do you get ?

Answer 12

i got a line that missed all the points, or a bendy line,

Answer 13

Yes, I got the same result. . .

Answer 14

it can't be a direct variation then

Answer 15

a direct variation would be a straight line,

all the ratios you calculated would have had to be the same

Answer 16

Oh, so y doesn't vary with x, there is no function rule?

Answer 17

y does vary with x, but it is not a direct variation,
it might be a quadratic , or a higher order curve its hard to tell with only three points

Answer 18

but you can tell for certain, that if there is a function that does contain those points it will not be of the form

y(x) = mx+b

Answer 19

for y to not vary with x, would be something like

(x, y) = (0,4), (1,4), (500,4)

here y is constant

y(x) = 4

Answer 20

Okay, what about (1,1), (2,2), (5,5)? I got a strong positive correlation. This would be a direct variation?

Answer 21

yeah those all fit on a nice straight line,

can you tell me what the linear function is that contain those points?

y(x) =

Answer 22

Mmm, don't know. . .y(x)=8?

Answer 23

(1,1), (2,2), (5,5)

y(1) = 1
y(2) = 2
y(5) = 5
y(x) =

Answer 24

1?

Answer 25

its a straight line, so it will be of the form
y(x) = mx+b

Answer 26

the line that contains
the points (1,1), (2,2), (5,5)
is
y(x) = x

Answer 27

y(x) = 5?