How does the graph of f(x) = (x + 7)^3 – 8 compare to the parent function g(x) = x^3?

ANSWER

7 units left, 8 units down

EXPLANATION

The given function is

This is a function obtained by applying two transformations to the parent function,

The transformations are of the form

This transformation with shift the graph of the parent function k units to the left and c units down.

Therefore f(x) is the graph of g(x) shifted to the left 7 units and down 8 units.

Parent function is shifted 7 units left then 8 units down to produce

.

Step-by-step explanation:

Given polynomial is and it's parent function is .

Now we need to determine about how does the graph of f(x) compare to the parent function g(x).

We know that f(x+h) indicates left shift by h units.

then f(x+7) indicates 7 units left shift.

We know that f(x)-k indicates down shift by k units.

then f(x)-8 indicates 8 units down shift.

So finally we can say that parent function is shifted 7 units left then 8 units down to produce

.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

what are you trying to solve here

step-by-step explanation: