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Find an equation for the graph sketched below and explain how you got it.

Find an equation for the graph sketched below and explain how you got it.-example-1

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The equation of the function graphed is y = (4) ˣ - 2

How to find the equation

The equation is an exponential function which is written of the form

y = a (b) ˣ

From the graph we translate the figure up 2 units to return to the preimage. At this point we have that points (0, 1) and (1, 4) on the graph

so that using (0, 1)

y = a (b) ˣ (b exponent of 0 is 1)

1 = a 1

a = 1

Using (1, 4) to solve for b

y = a (b) ˣ

4 = 1 (b) (b exponent of 1 is b)

b = 4

The equation is y = (4) ˣ then will translate it to revere the initial procedure

y = (4) ˣ - 2

User Hrant
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