Question

Using y= bx [exponential function] as the parent function, make your own transformations (3 units right, reflect on x axis, 2 units down). Then graph and state domain and range.

Answer 1

$y=b^x$

Let's say for example, our parent function is:

$y=2^x$

Let's start doing the given transformation in the question.

1. Horizontal shift 3 units to the right. We shift to the right by subtracting x units on the x-variable.

$y=2^{x-3}$

2. Reflect on the x-axis. We reflecting by adding a negative sign on the function.

$y=-2^{x-3}$

3. Vertical shift 2 units down. We are going to subtract 2 on the whole function.

$y=-2^{x-3}-2$

The graph of the parent and new function is shown below:

The domain and range of this function are:

Domain: All real numbers

Range: y < -2 or from negative infinity to -2. In interval notation, we have:

$(-\infty,-2)$