Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

a line labeled f of x passing through 0, negative 1 and 3, 1
x g(x)
0 3
2 6
4 9
the slope of f(x) is greater than the slope of g(x).
the slope of f(x) is less than the slope of g(x).
the slope of f(x) is equal to the slope of g(x).
the slope of g(x) is undefined.

The slope of f(x) is less than the slope of g(x).

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

step 1

Determine the slope of f(x)

we have the points

(0,-1) and (3,1)

substitute the values in the formula

step 2

From the data in a table  take two points

(0,3) and (2,6)

substitute the values in the formula

step 3

Compare the slopes

therefore

The slope of f(x) is less than the slope of g(x).

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: