The function y = rootindex 3 startroot x endroot – 3 is graphed only over the domain of {x | –8 < x < 8}. what is the range of the graph?

{y | –5 < y < 5}
{y | –5 < y < –1}
{y | 1 < y < 5}
{y | 1 < y < –1}

Explanation:

The graphed function is:

And it is graphed over the domain {x | –8 < x < 8}, which is all the real numbers greater than - 8 and less than 8.

The cube root is a continuous growing function over all the real numbers.

Thus, to find the range you can just substitute the border numbers, -8 and 8, into the function, to find the corresponding y-values.

For x = - 8:

For x = 8

Hence, the range is {y | –5 < y < -1} ← answer

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what is the image?

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: