Graph Exponential Functions

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Presentation transcript:

Graph Exponential Functions

exponential functions Remember that Exponential Functions: Take the form y = abx (or y = ax m) Graph as a smooth curve ‘growth’ = increasing ‘decay’ = decreasing they will get big fast! like geometric sequences

Exponential Functions

Graph Exponential Functions -3 -2 -1 1 2 3 2-3 = 1 23 = 1 8 1 8 Sketch the graph of y = 2x 2-2 = 1 22 = 1 4 1 4 Make a table of values (be careful with your exponent rules) Plot them on a graph Connect with a smooth curve (Remember the asymptote! Don’t let your curve go totally straight, but also don’t let it keep going down forever) 2-1 = 1 21 = 1 2 1 2 20=1 1 21=2 2 22=4 4 23=8 8 Since y=abx then here it is y=(1)(2)x so the y-int is 1 and the constant ratio is 2 (notice the y values in table are doubling) Will it ever touch the x-axis?

Graph Exponential Functions -3 -2 -1 1 2 3 2-3 = 1 8 +4 4 1 8 Sketch the graph of y = 2x + 4 2-2 = 1 4 +4 4 1 4 Make a table of values (be careful with your exponent rules) Plot them on a graph Connect with a smooth curve (Remember the asymptote! Here it will be the line y=4. Why?) 2-1 = 1 2 +4 4 1 2 20=1+4 5 21=2+4 6 22=4+4 8 23=8+4 12

sketching an accurate curve Remember the asymptote! Don’t let your curve go totally straight, but also don’t let it keep going down forever

Graph Exponential Functions -3 -2 -1 1 2 3 3-3 = 1 33 = 1 27 1 27 Sketch the graph of y = 3x 3-2 = 1 32 = 1 9 1 9 Make a table of values (be careful with your exponent rules) Plot them on a graph Connect with a smooth curve (Remember the asymptote! Don’t let your curve go totally straight, but also don’t let it keep going down forever) 3-1 = 1 31 = 1 3 1 3 30=1 1 3 9 27 Will it ever touch the x-axis?

Graph Exponential Functions -3 -2 -1 1 2 3 ( 𝟏 𝟐 )-3 = 1−3 2−3 = 23 13 =8 8 Sketch the graph of y = ( 1 2 )x 4 ( 𝟏 𝟐 )-2 = 1−2 2−2 = 22 12 =4 2 Make a table of values (be careful with your exponent rules) Plot them on a graph Connect with a smooth curve 1 ( 𝟏 𝟐 )-1 = 1−1 2−1 = 21 11 =2 1 2 1 4 1 8 How can you predict from the function that this is a decreasing graph?