Question

What is the equation of the graph obtained when the parent graph y=x^3 translated 4 units left and 7 units down?

Answer 1

y = (x + 4)³ - 7

Further explanation

There are four types of transformation geometry:  

• translation (or shifting),  
• reflection,  
• rotation, and  
• dilation (stretching or shrinking).  

In this case, the transformation is shifting vertically and horizontally.

• Translation (or shifting): moving a graph on an analytic plane without changing its shape.  
• Vertical shift: moving a graph upwards or downwards without changing its shape.  
• Horizontal shift: moving a graph to the left or right downwards without changing its shape.  

Vertical Shift

Given the graph of y = f(x) and v > 0, we obtain the graph of:  

• $\boxed{ \ y = f(x) + v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ upward v units.  
• $\boxed{ \ y = f(x) - v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ downward v units.  

Horizontal Shift

Given the graph of y = f(x) and h > 0, we obtain the graph of:  

• $\boxed{ \ y = f(x + h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the left h units.  
• $\boxed{ \ y = f(x - h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the right h units.

- - - - - - - - - -

Given:

The parent graph $\boxed{ \ y = x^3 \ }$

Question:

What is the equation of the graph obtained when the parent graph y=x^3 translated 4 units left and 7 units down?

The Process:

Clearly, we must translate the graph of $\boxed{ \ y = x^3 \ }$ to obtain the new equation of the graph.

$\boxed{ \ y = x^3 \ }$ translated 4 units left.

It becomes $\boxed{ \ y = (x + 4)^3 \ }$

Furthermore, $\boxed{ \ y = (x + 4)^3 \ }$ translated 7 units down.

Thus, the result is $\boxed{ \ y = (x + 4)^3 - 7 \ }$

Conclusion

Thus, when the parent graph of y = x³ translated 4 units left and 7 units down, the result is the equation of the graph y = (x + 4) ³ - 7

Learn more  

1. Transformations that change the graph of f(x) to the graph of g(x) brainly.com/question/2415963
2. The similar problem brainly.com/question/1369568
3. Which equation represents the new graph brainly.com/question/2527724

Keywords: what is the equation, the graph, y = x³, which, correctly, y = (x + 4)³ - 7, obtained, when ,the parent, translation, shift, left, down, up, upward, units, horizontal, vertical , transformation

Answer 2

Answer:

y = (x + 4)³ - 7

Step-by-step explanation:

Parent function describes the general formula of a graph without a translation, or shift of any kind.  When considering how these shifts affect the graph, a translation to the left or right would affect the x-axis and a translation up or down would affect the y-axis.  When the x-axis is affected, that constant must be connected to the variable 'x', while a movement up or down must be separated and connected to the variable 'y'.  In the case of the parent function y = x³, adding '4' to the variable 'x' would shift the graph left and subtracting the '7' as a constant of the expression would move the graph down:

y = (x + 4)³ - 7