Exercise 39 Page 449

We want to write the exponential equation of the parent function represented by the graph. Then we will write a function for the indicated translation. Let's approach these tasks one at a time.

Writing the Equation for the Parent Function

Exponential functions all follow the same general form. y=ab^x By identifying two points on the given graph, we can use them to determine the equation of parent function.

The points (0,-1) and (1,-3) both lie on the curve. Notice that (0,-1) is the y-intercept. We can substitute the y-intercept into the formula to solve for a.

Having found a, we can substitute this into the general form. y=-1* b^x ⇔ y=- b^x Next, we can substitute x=1 and y=-3 into the above equation, and solve for b.

Finally, we can write the parent function represented by the graph. y=-3^x

Function for the Indicated Translation

Now, we want to write a function for the indicated translation. 8 units right and 2 units up To do so, we should recall two things.

• If a horizontal translation is to the right, we subtract from the x-variable. If the translation is to the left, we add to the x-variable.
• If a vertical translation is up, we add to the y-variable. If the translation is down, we subtract from the y-variable.

Therefore, for the indicated translation, we have to subtract8 from the x-variable and add4 to the entire function. y=-3^(x - 8) + 4