Exponential function
An
exponential function
has the form
$f(x) = Ab^x$ \gap[40] \t
Function form
\\ $y= Ab^x$ \gap[40] \t
Equation form
where $A$ and $b$ are constants with $b$ positive. We call $b$ the
base
of the exponential function.
Technology formula
:
A*b^x
Examples
1.
\t $f(x) = 2^x$ \t
$A = 1, b = 2$
\gap[20] \t Technology:
2^x
\\ \t $f(3) = 2^3 = 8$ \\ \t $f(0) = 2^0 = 1$ \\ \t $\displaystyle f(-4) = 2^{-4} = \frac{1}{2^4} = \frac{1}{16}$ \\ \\
2.
\t $g(x) = 10(1.5^x)$ \t
$A = 10, b = 1.5$
\gap[20] \t Technology:
10*1.5^x
\\ \t !2! $g(2) = 10(1.5^2) = 10(2.25) = 22.5$ \\ \t $g(-1) = 10(1.5^{-1}) = \frac{10}{1.5} = \frac{20}{3}$ \\ \\
3.
\t $h(x) = 4(3^{2x})$ \t
Rewrite this as
$4((3^2)^x) = 4(9^x)$
\gap[20] \t Technology:
4*3^(2x)
\\ \t \t
$A = 3, b = 9$
One for you
Let $f(%1)=%0[1].$ Fill in the following table of exact values of $f$.
$\bold{%1\ }$ \t $\bold{f(%1) = %0[1]}$ \\ $-3$ \t BOX \\ $-2$ \t BOX \\ $-1$ \t BOX \\ $0$ \t BOX \\ $1$ \t BOX \\ $2$ \t BOX \\ $3$ \t BOX
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In the graph of $f(%1)= %0[1]$, the $y$-intercept is BOX and the value of $y$ is multiplied by BOX for every 1-unit increase of $x$.
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#[Now choose the correct graph of $f$.][Ahora escoge la gráfica correcta de $f$.]#
MULTIPLECHOICE
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RANDOMIZE