Question

A classmate claims that the function g(x)=-4ex+6 is the parent function f(x)=ex reflected across the Y axis, vertically compressed by a factor of four, translated to the left five units, and translated up six units.A) explain what the classmate described incorrectly.B) describe g(x) as a series of transformations of f(x)

Answer 1

Based on the function g(x), the function f(x) is multiplied by a negative number. Hence, there is a reflection across the x-axis.

If it was the "x" variable that was multiplied by a negative number for example, y = e^-x, it would have been reflection across the y-axis.

Since the number multiplied to the function f(x) is not between 0 and 1, we are stretching the function. Hence, the function is vertically stretched by a factor of 4.

Moving to the number -5 that was subtracted from the variable x, we have moved/shifted the function 5 units to the right instead of left.

Lastly, 6 was added to the entire function, therefore, we have translated the functions 6 units up.

To summarize, f(x) = e^x had undergone the following series of transformation: reflection across the x-axis, vertically stretched by a factor of 4, translated 5 units to the right, and translated 6 units up to form g(x).