The table shows a linear function. x 5 4 3 2 1
0 1 2 3
f x  11 3
5 13 21 29 37 45 53
(a) Determine the difference of outputs of any two inputs that are 1 unit apart. Show your work.
(b) Determine the difference of outputs of any two inputs that are 2 units apart. Show your work.
(c) Determine the difference of outputs of any two inputs that are 3 units apart. Show your work.
(d) What do you notice about the ratios of the differences in the outputs to the input intervals? Explain
your answer.

a) I used the equation x=-5; f(x)=-11 and x=-4; f(x)=-3. We get the range = -3-(-11)=8

b) I used the equation x=-5; f(x)=-11 and x=-3; f(x)=5. We get the range = 5-(-11)=16

c) I used the equation x=-5; f(x)=-11 and x=-2; f(x)=13. We get the range = 13-(-11)=24

d) Range of input is equal with the ratios of the output. You can find the pattern of output above 8,16,and 24 can divided by 8 and give the result 1,2 and 3

f

step-by-step explanation:

f

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source: