#### Find the domain and the range of the exponential function

f(x)= -3^{(x+1)}+3

ccss.hsa1ef-qx.9
exponential functions
domain and range of exponential functions
ninth grade
high-school
Algebra

Anonymous

0

f(x)= -3^{(x+1)}+3

Sangeetha Pulapaka

0

STEP 1: Recall how to graph an exponential function

https://www.varsitytutors.com/hotmath/hotmath_help/topics/graphing-exponential-functions

STEP 2: Graph the given exponential function

The horizontal asymtote of the given exponential function is at y = 3 and since a<0 the graph will lie below y = 3

So, draw a horizontal line at y = 3 and move down

STEP 3: Recall what is the domain and the range of a function

https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/find-domain-and-range-from-graphs/

Domain is got by taking the x-coordinates of the left most point and the x-coordinates of the right most point. Range is got by taking the y-coordinate of the lowest point to the y-coordinate of the highest point.

The graph covers the x-values from \infty to -\infty since as you can see the graph moves infinitely to the left and to the right of the x-axis.

So, the domain is represented by D: (\infty , - \infty)

The range are the values of y from the bottom most point on the y-axis and the upmost point of the y-axis The graph move infinitely to the bottom and has a horizontal asymtote at y = 3.

So, the range will be R: (-\infty, 3)

Skills you may further want to recall:

What is an exponential function

https://www.purplemath.com/modules/expofcns.htm

What is the horizontal asymtote of an exponential function

https://magoosh.com/hs/ap-calculus/2017/find-horizontal-asymptotes/