a) Z wykresu odczytujemy, że:

$f\left(1\right)=3=3^1$  

$f\left(2\right)=9=3^2$  

Zatem a=3.

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Wzór funkcji: f(x)=3^x.

$x$	$2$	$1$	$-1$	$-3$
$y$	$9$	$3$	$\frac{1}{3}$	$\frac{1}{27}$

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Sprawdzenie:

$f\left(2\right)=3^2=9$  

 

$f\left(1\right)=3^1=3$  

 

$3^x=\frac{1}{3}$  

$3^x=3^{-1}$  

$x=-1$  

 

$3^x=\frac{1}{27}$  

$3^x=3^{-3}$  

$x=-3$  

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b) Z wykresu odczytujemy, że:

$f\left(-1\right)=4={\left(\frac{1}{4}\right)}^{-1}$  

Zatem a=¹/₄.

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Wzór funkcji: $f\left(x\right)={\left(\frac{1}{4}\right)}^x.$

$x$	$-2$	$0,5$	$2$	$-\frac{1}{2}$
$y$	$16$	$\frac{1}{2}$	$\frac{1}{16}$	$2$

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Sprawdzenie:

$f\left(-2\right)={\left(\frac{1}{4}\right)}^{-2}=4^2=16$  

 

$f\left(0,5\right)={\left(\frac{1}{4}\right)}^{0,5}={\left(\frac{1}{4}\right)}^{\frac{1}{2}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$  

 

${\left(\frac{1}{4}\right)}^x=\frac{1}{16}$  

${\left(\frac{1}{4}\right)}^x={\left(\frac{1}{4}\right)}^2$  

$x=2$  

 

${\left(\frac{1}{4}\right)}^x=2$  

${\left(\frac{1}{4}\right)}^x={\left(\frac{1}{2}\right)}^{-1}$  

${\left(\frac{1}{4}\right)}^x={\left(\sqrt{\frac{1}{4}}\right)}^{-1}$  

${\left(\frac{1}{4}\right)}^x={\left(\frac{1}{4}\right)}^{-\frac{1}{2}}$  

$x=-\frac{1}{2}$