Ashipping company charges based on calculations of the volume of a rectangular box and the sum of the dimensions of the
box. a square rectangular prism has a side length represented by the linear function f(x), and a height represented by the
linear function g(x).
x
3
4
8
v(x) = (f f-g)(x) s(x) = (f+f+g)(x)
15
2410
35
12
48
which statement describes the combined functions v(x) and s(x)?
the volume function is linear but the sum function is not
the sum function is linear but the volume function is not
both the volume function and the sum function are linear
neither the volume function nor the sum function is linear

B. The sum function is linear but the volume function is not

Step-by-step explanation:

We are given that f(x) and g(x) are linear. Due to this, the sum function S(x) is linear.

And we know the shape of our figure, so we just need to multiply the dimensions for V(x) but the product of three linear functions results in a cubic function, and we conclude V(x) is not linear.

Glad to answer.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: