Question

On the coordinate grid, the graph of y = RootIndex 3 StartRoot x minus 1 EndRoot + 3 is shown. It is a translation of y = RootIndex 3 StartRoot x EndRoot. On a coordinate plane, a cube root function goes through (negative 7, 1), has an inflection point at (1, 3), and goes through (2, 4). What is the domain of the graphed function? {x | 1 < x < 5} {y | 1 < y < 5} {x | x is a real number} {y | y is a real number}

Answer 1

Answer

{x | x is a real number}

Step-by-step explanation:

The equation of the given graph is

$y = \sqrt[3]{x - 1} + 3$

This is a cube root function that has been shifted 1 unit left and 3 units up.

The is the set of all values that makes the function defined.

The domain of the parent function is all real numbers.

So the domain of the transformed function is also all real numbers.

Answer 2

The domain of a graph is the set of input values the function can take

The domain of the graphed function is (c) {x | x is a real number}

The equation of the graph is given as:

$y = \sqrt[3]{x -1} + 3$

The above function is a cubic function, and a cubic function can take any real number as its input

This means that, the input values of the function $y = \sqrt[3]{x -1} + 3$ is the set of real numbers

Hence, the domain of the graphed function is (c) {x | x is a real number}

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