55. Graphing Exponential Functions

Steps to draw a graph Draw the asymptote In your calculator, make a table with the starting x value that makes the exponent = 0 Plot points Connect with a smooth curve that approaches asymptote on one side and infinity or – infinity on the other

Graph y = x 2 +0 1. Draw an asymptote 2. Start table at x = 0

draw a curve that “hugs” the x-axis, and moves up to the right. 0, 1 2 EXAMPLE 2 Graph the function. x 1 y ½ 2 1. Draw the asymptote Plot and (1, 2) draw a curve that “hugs” the x-axis, and moves up to the right. 0, 1 2 2.

EXAMPLE 3 Graph the function. 5 y = – 2 Draw the asymptote 5 1 y -1 -5/2 y = – 5 2 x Draw the asymptote Plot (0, –1) and . Draw a curve that begins just below the x-axis, and moves down to the right. 1, – 5 2

EXAMPLE 4 Graph the function. x 1 Graph y = 2 +1 4 Draw the asymptote 1 y 3 3/2 Graph y = 2 1 4 x +1 Draw the asymptote Plot (0, 3) and . draw a curve that begins just above the x-axis and moves up to the left. 1, 3 2

-2 EXAMPLE 5 Graph y = –3 2 5 x Draw the asymptote 1, –3.2 1 y -5 -3.2 -2 Draw the asymptote 1, –3.2 Plot (0, –5) and Draw a curve that begins just below the x-axis, and moves down to the left.

Example

Example

Review: Characteristics of Exponential Functions Domain: Range: Asymptotes: Zeros: Intercepts: Intervals of Increase and Decrease: End Behaviors: Transformations: