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How does the graph of g(x) = −(x + 3)4 compare to the parent function of f(x) = x4?

g(x) is shifted 3 units to the right and 1 unit up.
g(x) is shifted 3 units to the right and 1 unit down.
g(x) is shifted 3 units to the right and reflected over the x-axis.
g(x) is shifted 3 units to the left and reflected over the x-axis.

Respuesta :

profantoniofonte

Answer:

g(x) is shifted 3 units to the left and reflected over the x-axis.

Step-by-step explanation:

Given the Parent function:

[tex]x^{4}[/tex]

And the other

[tex]g(x)=-(x+3)^4[/tex]

Since the g(x) function is multiplied by -(1) and added to 3 units, then the curve is translated 3 units left and reflected over the x-axis, as the graph below shows.

The negative parameter "a" reflects over the x-axis. And the independent parameters, being added to the parent one translate the curve.

Ver imagen profantoniofonte

The difference between the functions f(x) and g(x) is the addition of a

constant to the value of x and changing the sign of the output.

The graph of g(x) compared to f(x) is g(x) is shifted 3 units to the left and

reflected over the x-axis.

Reason:

The addition of a positive constant term to the input variable of a function,

shifts the graph to the left of the graph of the parent function.

Please find attached the image of the graph of f(x), which is g(x) shifted to

the left by 3 units.

Changing the sign of the output value from positive to negative;

When the output value of a function is changed from positive to negative,

and vice versa, it is equivalent to a reflection across the x-axis.

Therefore, the function g(x) is a reflection across the x-axis.

Therefore;

g(x) is shifted 3 units to the left and reflected over the x-axis.

Learn more here:

https://brainly.com/question/6701068

Ver imagen oeerivona

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