Draw a graph for each expression. a) f(x) = 2^{x} b) f(x) = 2^{-x} c) f(x) = - 2^{x} d) f(x) = -2^{-x}

Question

Draw a graph for each expression.
a)

f (x) = 2^{x}

b)

f (x) = 2^{- x}

c)

f (x) = - 2^{x}

d)

f (x) = - 2^{- x}

Answer 1

Step 1
Properties of exponential function $a^{x}, a > 1$
1. Has continuous and smooth graph.
2. The graph passes through (0, 1) point.
3. The graph is increasing and it increases without bound.
4. Domain is whole real line.
5. Range is $[0, \infty]$
Step 2
a) The graph of $f (x) = 2^{x}$ is:

Step 3
b) The graph of $f (x) = 2^{- x}$ is obtained by taking reflection of the graph of
$f (x) = 2^{x}$ about y - axis.
Therefore, graph of $f (x) = 2^{- x} :$

c) The graph of $f (x) = - 2^{x}$ is obtained by taking reflection of the graph of
$f (x) = 2^{x}$ about x - axis.
Therefore, graph of $f (x) = - 2^{x} :$

d) The graph of $f (x) = - 2^{- x}$ is obtained by taking reflection of the graph of
$f (x) = 2^{- x}$ about x - axis.
Therefore, graph of $f (x) = - 2^{- x} :$

Draw a graph for each expression. a) f(x) = 2^{x} b) f(x) = 2^{-x} c) f(x) = - 2^{x} d) f(x) = -2^{-x}

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