Resource 9 - Exponential Functions - Worked Solution



Exponential functions What do the graphs look like?Use Desmos or other graphing software to graph the following and look at the shape of the graphs.y=2xy=10xy=5xy=3-xy=1.1-xy=8-xDefinitionAll the above graphs are exponential functions.An exponential function is a function in the form y=ax and y=a-x, where (a>0)By looking at the graphs drawn above, complete the statements about the shape of an exponential function.If the function is in the form y=ax:The graph goes through the y axis at 1As x values get more negative, the y values approach zeroAs x values get more positive, the y values get really bigAs a gets bigger, the graph becomes closer to the y-axis/steeperIf the function is in the form y=a-x:The graph goes through the y axis at 1As x values get more negative, the y values get really bigAs x values get more positive, the y values approach zeroAs a gets bigger, the graph becomes closer to the y-axis/steeperUsing the informationUsing the definition of the function, choose which of the following are exponential functions:y=x2Noy=4xYesy=x2Noy=1.5-x YesBy looking at the shape of the graphs of the above functions, choose which of the following are exponential functions:YesNoNoNoYesYesMatch the equation with its graph:y=1.5xy=1.2-xy=7-xy=4xComplete the following table of values and use the points to graph the exponential curve.y=3xx-3-2-1012y127≈0.03719=0.1130.3139y=3x when x=-3y=3-3=127=0.037On the calculator:Plot as (-3, 0.037)y=3x when x=-3y=3-3=127=0.037On the calculator:Plot as (-3, 0.037)y=3x when x=1y=31=3On the calculator:y=3x when x=1y=31=3On the calculator:Plot each point.Join the plotted points with a curved line.Note – To make a smooth curve, place your wrist on the paper on the inside of the curve and use it as a pivot point when drawing. Try graphing these:y=2xx-2-1012y0.250.5124y=3-xx-2-1012y9310.30.1 ................
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