Lesson 47 Graphing exponential functions Exponential function y

Lesson 47 Graphing exponential functions

Exponential function y= x ab is an l A function of the form exponential function if x is a real number and a is not 0, and b>0 and b is not 1. l The parent function of all exponential functions is y= x b

Parent function y= x b , b>1

Parent function y = bx , 0<b<1

asymptote l l For each of the previous graphs, the line y= 0( the x-axis) is an asymptote. An asymptote is a line that a graph approaches as the value of a variable gets extremely large or small. The line y = k is a horizontal asymptote of a graph if y approaches k as x increases or decreases without bound. The base of an exponential function must be positive, but the exponent can be negative

Graph exponential functions with negative exponents l l Change to positive exponent by using the property: b-m = 1 m b 2 -3 = 1 2 3

Graphing y = bx l l l l Graph y = 2 x Identify the domain, range and asymptotes Make a table, plot the ordered pairs, and draw a curve through the points. x -3 -2 -1 0 1 2 3 2 x 1/8 1/4 1/2 1 2 4 8 Domain is all real numbers Range is all positive real numbers Asymptote is line y =0, since the graph gets closer and closer to the x-axis

Graph, identify the domain, range and asymptotes l y = 3 x l y = 4 x

Graphing y = bx and y = (1/b)x l l Graph y = 2 x and y = (1/2)x How are the graphs related?

Transformations of parent function

graph l l l y = 3 x y = (1/4) 3 x -2 What is the domain of all graphs? What is the range of all graphs? What are the asymptotes?

Graph y = ex and y = -ex

Graph y = 3 x and y = -3 x l l What is the domain of each? What is the range of each? What are the asymptotes of each? How are the graphs related?

Use calculator l l Graph y 1 = (1. 4)x y 2 = -(1. 4)x y 3 = -2(1. 4)x Describe the graphs

Application- interest l l The amount A in an account that earns interest is given by the exponential function A = P( 1 + r/n ) nt, where P is the initial deposit, r is the annual interest rate, n is the number of times per year the interest is compounded, and t is the number of years. Suppose $20, 000 is deposited in a college savings account when a person is born. How much will be in the account on that person's 18 th birthday if the account earns 9% compounded quarterly?