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Given the parent graph f(x)=e^x, which of the following functions has a graph that has been translated 3 to the left and reflected over the x-axis?following functions given to pick from are g(x)=−e^x+3g of x is equal to negative e raised to the x plus 3 powerg(x)=e^−(x+3)g of x is equal to e raised to the negative open paren x plus 3 close paren powerg(x)=e^3−xg of x is equal to e raised to the 3 minus x powerg(x)=−e^3−x

Sagot :

Given the parent function:

[tex]f(x)=e^x[/tex]

Let's determine the function that has a graph which has been translated 3 units to the left and reflected over the x-axis.

To find the function, apply the transformation rules for functions.

• After a translation 3 units to the left, we have:

[tex]g(x)=e^{x+3}[/tex]

• Followed by a reflection over the x-axis:

[tex]g(x)=-e^{x+3}[/tex]

Therefore, the function that has a graph which has been translated 3 units to the left and reflected over the x-axis is:

[tex]g(x)=-e^{x+3}[/tex]

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