How do you write an exponential function whose graph passes through the points (0,-18) and (-2,-2)?

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Answer 1 · 2017-11-15T18:55:59

We can have

$g (x) = - 18 {(3)}^{x}$ $g(x) = -18(3)^x$

An exponential function is given by $y = a (b^{x})$ $y = a(b^x)$ .

Setting up a system of equations, we have:

$- 18 = a b^{0}$ $-18 = ab^0$
$- 2 = a b^{- 2}$ $-2 = ab^(-2)$

We can immediately see from the first equation that $a = - 18$ $a= -18$ because $b^{0} = 1$ $b^0 =1$ .

$- 2 = - 18 b^{- 2}$ $-2 = -18b^(-2)$

$- 2 = - \frac{18}{b^{2}}$ $-2 = -18/b^2$

$b^{2} = 9$ $b^2 = 9$

$b = \pm 3$ $b = +- 3$

But $b > 0$ $b >0$ .

So the only plausible function is $y = - 18 {(3)}^{x}$ $y = -18(3)^x$ . We confirm graphically:
enter image source here

Hopefully this helps!