How does the graph of f(x) = (x + 7)3 − 8 compare to the parent function g(x) = x3?

The graph of f(x) is the translation of the graph of g(x) 7 units at left and 8 units down

Step-by-step explanation:

we have

---> The turning point is the point (0,0)

---> The turning point is the point (-7,-8)

so

The rule of the transformation of g(x) to f(x) is equal to

(x,y) ----> (x-7,y-8)

That means----> The translation is 7 units to the left and 8 units down

therefore

The graph of f(x) is the translation of the graph of g(x) 7 units at left and 8 units down

see the attached figure to better understand the problem

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d