write an equation for the function in the form $f(x) = a(b)^x$. use whole numbers, decimals, or simplified…

Explanation:

Step1: Find the value of ( a )

We know that the function is in the form ( f(x) = a(b)^x ). When ( x = 0 ), ( f(0) = -1 ) (from the point ( (0, -1) )). Substitute ( x = 0 ) and ( f(0) = -1 ) into the function: ( f(0) = a(b)^0 ) Since ( b^0 = 1 ) for any ( b \neq 0 ), we have ( -1 = a(1) ), so ( a = -1 ).

Step2: Find the value of ( b )

Now we know ( a = -1 ), and we also have the point ( (1, -7) ). Substitute ( x = 1 ), ( f(1) = -7 ), and ( a = -1 ) into the function ( f(x) = a(b)^x ): ( -7 = -1(b)^1 ) Simplify the equation: ( -7 = -b ), so ( b = 7 ).

Step3: Write the function

Now that we have ( a = -1 ) and ( b = 7 ), substitute these values back into the form ( f(x) = a(b)^x ): ( f(x) = -1(7)^x ) or ( f(x) = -7^x )

Answer:

( f(x) = -7^x ) (or ( f(x) = -1 \times 7^x ))