Question

geogebra.org/lti/launch
move the two points to define
an exponential function and
then enter the function below.

f(x) =
(1,2)
(-3,1)
-4 -3 -2 -1 0 1 2 3 4
-1
-2
-3
-4
-5

Explanation:

Step1: Assume exponential form

Let \( f(x) = ab^x \), where \( a,b>0,b
eq1 \).

Step2: Substitute (-3,1)

\( 1 = ab^{-3} \implies a = b^3 \).

Step3: Substitute (1,2)

\( 2 = ab^1 \). Substitute \( a = b^3 \): \( 2 = b^3 \cdot b = b^4 \).

Step4: Solve for b

\( b = 2^{1/4} = \sqrt[4]{2} \).

Step5: Find a

\( a = (\sqrt[4]{2})^3 = 2^{3/4} = \sqrt[4]{8} \).

Step6: Write function

\( f(x) = 2^{3/4} \cdot 2^{x/4} = 2^{(x+3)/4} \).

Answer:

\( 2^{(x+3)/4} \) (or equivalent form like \( \sqrt[4]{8} \cdot \sqrt[4]{2}^x \))