Graphing Exponential Functions Exponential Growth p 635 CCSS IF .8

Definition An exponential function is a function of the form f (x) = bx, where the base b is a positive constant other than I and the exponent x is a variable.

Explore: Graphing and Analyzing f(x) = 2x and f(x) = 10x Complete the table x f(x) = 2x – 3 – 2 – 1 1 2 3 x f(x) = 10x – 3 – 2 – 1 1 2 3

Graph the parent functions. y = 2x y = 10x x

What is the domain and range of each function? Domain of y = 2x : {x| } y = 10y : {x| } Range of y = 2x : {x| }

What is the y- intercept of each function? y- intercept of y = 2x : y-intercept of y = 10x : What is the trend of each function? In both cases, as the value of x increases, the value of y ……………………

g(x) = a(bx – h) + k k represents the vertical translation h represents the horizontal translation a represents either the vertical stretch or compression a < 0 : parent function is reflected across the x-axis (0, 1) becomes (h, a+ k) and (1, b) becomes (1 + h, ab + k) Asymptote is y = k

Describe the effect of each transformation on the parent function Describe the effect of each transformation on the parent function. Graph the parent function and its transformation. Then determine the domain, range, and y-intercept of each function 1. f(x)= 2x and g(x)= 2(2x)

2. f(x) = 2x and g(x)= – 5(2x)

3. f(x) = 2x and g(x)= 2x+2

4. f(x) = 2x and g(x)= 2x + 5