Exercise 38 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 and the general form shown above to determine the equation of parent function.

The points (0,4) and (1,2) both lie on the curve. Notice that (0,4) 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=4b^x Next, we can substitute x=1 and y=2 into the updated equation to solve for b.

Finally, we can write the parent function represented by the graph. y=4( 1/2 )^x

Function for the Indicated Translation

Now, we want to write a function for the indicated translation. left4 units and up3 units 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 add4 to the x-variable and add3 to the entire function. y=4( 1/2 )^(x + 4) + 3