Question

Describe the transformations from the parent function y=3ˣ. y=-2*3ˣ⁺²+5

Answer 1

The function y = -2*3^(x+2)+5 is obtained by applying transformations to the parent function y = 3^x, which include a reflection, horizontal shift, and vertical shift.

Step-by-step explanation:

The given function is y = -2*3^(x+2)+5. This function is obtained by applying transformations to the parent function y = 3^x. Let's break down the transformations:

1. The function is multiplied by -2. This causes a reflection about the x-axis, which flips the graph upside down.
2. The exponent of x is changed to (x+2). This causes a horizontal shift of 2 units to the left.
3. The function is shifted vertically upwards by 5 units.

Overall, these transformations result in a flipped graph that is shifted 2 units to the left and 5 units upwards.