Question

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

Answer 1

Given the parent function:

`f(x)=e^x`

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:

`g(x)=e^(x+3)`

• Followed by a reflection over the x-axis:

`g(x)=-e^(x+3)`

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

`g(x)=-e^(x+3)`