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Challenges
Exponential Functions
Graph the following functions on Desmos above.
$f\left(x\right)=2^x$
$g\left(x\right)=3^x$
$h\left(x\right)=5^x$
$j\left(x\right)=\left(\frac{1}{2}\right)^x$
$k\left(x\right)=\left(\frac{1}{3}\right)^x$
$l\left(x\right)=0.2^x$
For $f\left(x\right)=a^x$ where $a>0$, the equation of the horizontal asymptote is:
Check
For $f\left(x\right)=a^x$ where $a>0$, the coordinates of the $y$-intercept are:
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The domain of $f\left(x\right)=a^x$ where $a>0$ is $x\in$
Check
.
The range of $f\left(x\right)=a^x$ where $a>0$ is $y\gt$
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$, y\in$
Check
.
Graph the following functions on Desmos above.
$f\left(x\right)=-2^x$
$g\left(x\right)=-3^x$
$h\left(x\right)=-5^x$
$j\left(x\right)=-\left(\frac{1}{2}\right)^x$
$k\left(x\right)=-\left(\frac{1}{3}\right)^x$
$l\left(x\right)=-0.2^x$
For $f\left(x\right)=-a^x$ where $a>0$, the equation of the horizontal asymptote is:
Check
For $f\left(x\right)=-a^x$ where $a>0$, the coordinates of the $y$-intercept are:
Check
The domain of $f\left(x\right)=-a^x$ where $a>0$ is $x\in$
Check
.
The range of $f\left(x\right)=-a^x$ where $a>0$ is $y\lt$
Check
$, y\in$
Check
.
Graph the following functions on Desmos above.
$f\left(x\right)=2^{-x}$
$g\left(x\right)=3^{-x}$
$h\left(x\right)=5^{-x}$
$j\left(x\right)=\left(\frac{1}{2}\right)^x$
$k\left(x\right)=\left(\frac{1}{3}\right)^x$
$l\left(x\right)=\left(\frac{1}{5}\right)^x$
$f\left(x\right)=a^{-x}=\Bigl($
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$\Bigl)$
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Check
Graph the following functions on Desmos above.
$f\left(x\right)=2^x+1$
$g\left(x\right)=2^x-4$
$h\left(x\right)=3^x+2$
$j\left(x\right)=-3^x-7$
$k\left(x\right)=\left(\frac{1}{5}\right)^x+3$
$l\left(x\right)=-5^{-x}-5$
For exponential functions of the form $f\left(x\right)=p\times a^{bx}+k$, the equation of the horizontal asymptote is
Check
.