The Exponential Curve

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Question 1 of 3

1. Question
Plot the graph for the equation $y = 3^{x}$ $y=3^x$ for $- 2 \leq x \leq 2$ $-2\leq x\leq 2$ .
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Create a table for $x$ $x$ and $y$ $y$ values and fill in values of $x$ $x$ , beginning with $- 2$ $-2$ in intervals of $0.5$ $0.5$ .

$x$ $x$ $- 2$ $-2$ $- 1.5$ $-1.5$ $- 1$ $-1$ $- 0.5$ $-0.5$ $0$ $0$ $0.5$ $0.5$ $1$ $1$ $1.5$ $1.5$ $2$ $2$

$y$ $y$

For each value of $x$ $x$ in the table, calculate $3^{x}$ $3^x$ and put this value in the cell below the $x$ $x$ -value.

For example $3^{- 2} = 0.11$ $3^-2=0.11$ , so fill this in the $y$ $y$ row, underneath the value $- 2$ $-2$ in the $x$ $x$ row.

The completed table should be as shown below.

$x$ $x$ $- 2$ $-2$ $- 1.5$ $-1.5$ $- 1$ $-1$ $- 0.5$ $-0.5$ $0$ $0$ $0.5$ $0.5$ $1$ $1$ $1.5$ $1.5$ $2$ $2$

$y$ $y$ $0.11$ $0.11$ $0.19$ $0.19$ $0.33$ $0.33$ $0.58$ $0.58$ $1$ $1$ $1.7$ $1.7$ $3$ $3$ $5.2$ $5.2$ $9$ $9$

Plot the points in the table on a set of coordinate axes.

For example the first column tells us the point $(- 2, 0.11)$ $(-2,0.11)$ should be plotted on the graph

Draw a smooth curve through these points.
Question 2 of 3

2. Question
Plot the graphs for the equations $y = 2^{x}$ $y=2^x$ and $y = 5^{x}$ $y=5^x$ for $- 2 \leq x \leq 2$ $-2\leq x\leq 2$ .
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Create a table for $x$ $x$ and $y$ $y$ values for both functions, and fill in values of $x$ $x$ between $- 2$ $-2$ and $2$ $2$ .

$y = 2^{x}$ $y=2^x$

$x$ $x$ $- 2$ $-2$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$

$y = 5^{x}$ $y=5^x$

$x$ $x$ $- 2$ $-2$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$

For each value of $x$ $x$ in the first table, calculate $2^{x}$ $2^x$ and put this value in the cell below the $x$ $x$ -value. Do the same with $5^{x}$ $5^x$ in the second table.

For example $2^{- 2} = 0.25$ $2^-2=0.25$ , so fill this in the $y$ $y$ row of the first table, underneath the value $- 2$ $-2$ in the $x$ $x$ row.

The completed tables should be as shown below.

$y = 2^{x}$ $y=2^x$

$x$ $x$ $- 2$ $-2$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$ $0.25$ $0.25$ $1$ $1$ $2$ $2$ $4$ $4$

$y = 5^{x}$ $y=5^x$

$x$ $x$ $- 2$ $-2$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$ $0.04$ $0.04$ $1$ $1$ $5$ $5$ $25$ $25$

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 $(- 2, 0.25)$ $(-2,0.25)$ should be plotted on the graph.

The point $(2, 25)$ $(2,25)$ does not fit on the axes.

Draw a smooth curve through each set of points.
Question 3 of 3

3. Question
Plot the graph for the equation $y = 2^{- x}$ $y=2^{-x}$ for $- 2 \leq x \leq 2$ $-2\leq x\leq 2$ .
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Create a table for $x$ $x$ and $y$ $y$ values, and fill in values of $x$ $x$ , between $- 2$ $-2$ and $2$ $2$ .

$x$ $x$ $- 2$ $-2$ $0$ $0$ $1$ $2$

$y$

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.

The Exponential Curve

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$x$ $x$	$- 2$ $-2$	$- 1.5$ $-1.5$	$- 1$ $-1$	$- 0.5$ $-0.5$	$0$ $0$	$0.5$ $0.5$	$1$ $1$	$1.5$ $1.5$	$2$ $2$
$y$ $y$