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What is the equation of y = x 3 y = x 3 with the given transformations? vertical stretch by a factor of 3, horizontal shift 4 units to the right, vertical shift 3 units down

Sagot :

Answer and Step-by-step explanation: In math, a graph, function or equation can be alterated - by shifting, reflecting, stretching or compressing - without losing its original shape. For example, a quadratic function maintains its parabolic shape when shifted.

When an equation is transformed vertically, it means its y-axis is changed. When it is horizontally, its x-axis is modified.

For equation [tex]y=x^{3}[/tex]:

  • Vertical stretch by a factor of 3:

This means the exponential equation will be multiplied by a constant, in this case 3. Then, the new equation is

[tex]y=3x^{3}[/tex]

  • Horizontal shift 4 units to the right:

When an equation is shifted, it's added a constant to it. As it is horizontal, it means it is added to the x and because it is to the right, it is a plus symbol:

[tex]y=x^{3+4}[/tex]

  • Vertical shift 3 units down:

Vertical shift means the equation is 3 units "below" the original equation, so:

[tex]y=x^{3}-3[/tex]

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