The Exponential Curve
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Question 1 of 3
1. Question
Plot the graph for the equation `y=3^x` for `-2\leq x\leq 2`.Hint
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Create a table for `x` and `y` values and fill in values of `x`, beginning with `-2` in intervals of `0.5`.`x` `-2` `-1.5` `-1` `-0.5` `0` `0.5` `1` `1.5` `2` `y` For each value of `x` in the table, calculate `3^x` and put this value in the cell below the `x`-value.For example `3^-2=0.11`, so fill this in the `y` row, underneath the value `-2` in the `x` row.The completed table should be as shown below.`x` `-2` `-1.5` `-1` `-0.5` `0` `0.5` `1` `1.5` `2` `y` `0.11` `0.19` `0.33` `0.58` `1` `1.7` `3` `5.2` `9` Plot the points in the table on a set of coordinate axes.For example the first column tells us the point `(-2,0.11)` should be plotted on the graph
Draw a smooth curve through these points.
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Question 2 of 3
2. Question
Plot the graphs for the equations `y=2^x` and `y=5^x` for `-2\leq x\leq 2`.Hint
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Create a table for `x` and `y` values for both functions, and fill in values of `x` between `-2` and `2`.`y=2^x``x` `-2` `0` `1` `2` `y` `y=5^x``x` `-2` `0` `1` `2` `y` For each value of `x` in the first table, calculate `2^x` and put this value in the cell below the `x`-value. Do the same with `5^x` in the second table.For example `2^-2=0.25`, so fill this in the `y` row of the first table, underneath the value `-2` in the `x` row.The completed tables should be as shown below.`y=2^x``x` `-2` `0` `1` `2` `y` `0.25` `1` `2` `4` `y=5^x``x` `-2` `0` `1` `2` `y` `0.04` `1` `5` `25` Plot the two sets of points in the table on a set of coordinate axes.For example the first column of the first table tells us the point `(-2,0.25)` should be plotted on the graph.
The point `(2,25)` does not fit on the axes.Draw a smooth curve through each set of points.
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Question 3 of 3
3. Question
Plot the graph for the equation `y=2^{-x}` for `-2\leq x\leq 2`.Hint
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Create a table for `x` and `y` values, and fill in values of `x`, between `-2` and `2`.`x` `-2` `0` `1` `2` `y` For each value of `x` in the table, calculate `2^{-x}`, taking great care with any negative signs, and put this value in the cell below the `x`-value.For example `2^{-(-2)}=2^2=4`, so fill this in the `y` row, underneath the value `-2` in the `x` row.The completed table should be as shown below.`x` `-2` `0` `1` `2` `y` `4` `1` `0.5` `0.25` Plot the points in the table on a set of coordinate axes.For example the first column tells us the point `(-2,4)` should be plotted on the graph
Draw a smooth curve through these points.