(-3,-2)

To find an exponential function, f(x)=ax, containing the point, set f(x) in the function to the y value -2 of the point, and set x to the x value -3 of the point.

-2=a-3

Rewrite the equation as a-3=-2.

a-3=-2

Rewrite the expression using the negative exponent rule b-n=1bn.

1a3=-2

Solve for a.

Multiply each term by a3 and simplify.

Multiply each term in 1a3=-2 by a3.

1a3⋅a3=-2⋅a3

Cancel the common factor of a3.

Cancel the common factor.

1a3⋅a3=-2⋅a3

Rewrite the expression.

1=-2⋅a3

1=-2a3

1=-2a3

Rewrite the equation as -2a3=1.

-2a3=1

Move 1 to the left side of the equation by subtracting it from both sides.

-2a3-1=0

Factor -1 out of -2a3-1.

Factor -1 out of -2a3.

-(2a3)-1=0

Rewrite -1 as -1(1).

-(2a3)-1⋅1=0

Factor -1 out of -(2a3)-1(1).

-(2a3+1)=0

-(2a3+1)=0

Multiply each term in -(2a3+1)=0 by -1

Multiply each term in -(2a3+1)=0 by -1.

-(2a3+1)⋅-1=0⋅-1

Simplify -(2a3+1)⋅-1.

Apply the distributive property.

(-(2a3)-1⋅1)⋅-1=0⋅-1

Multiply.

Multiply 2 by -1.

(-2a3-1⋅1)⋅-1=0⋅-1

Multiply -1 by 1.

(-2a3-1)⋅-1=0⋅-1

(-2a3-1)⋅-1=0⋅-1

Apply the distributive property.

-2a3⋅-1-1⋅-1=0⋅-1

Multiply.

Multiply -1 by -2.

2a3-1⋅-1=0⋅-1

Multiply -1 by -1.

2a3+1=0⋅-1

2a3+1=0⋅-1

2a3+1=0⋅-1

Multiply 0 by -1.

2a3+1=0

2a3+1=0

Subtract 1 from both sides of the equation.

2a3=-1

Divide each term by 2 and simplify.

Divide each term in 2a3=-1 by 2.

2a32=-12

Cancel the common factor of 2.

Cancel the common factor.

2a32=-12

Divide a3 by 1.

a3=-12

a3=-12

Move the negative in front of the fraction.

a3=-12

a3=-12

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

a=-123

Simplify -123.

Rewrite -12 as ((-1)3)312.

Rewrite -1 as (-1)3.

a=(-1)3123

Rewrite -1 as (-1)3.

a=((-1)3)3123

a=((-1)3)3123

Pull terms out from under the radical.

a=(-1)3123

Raise -1 to the power of 3.

a=-123

Rewrite 123 as 1323.

a=-1323

Any root of 1 is 1.

a=-123

Multiply 123 by 232232.

a=-(123⋅232232)

Combine and simplify the denominator.

Multiply 123 and 232232.

a=-23223232

Raise 23 to the power of 1.

a=-232231232

Use the power rule aman=am+n to combine exponents.

a=-232231+2

Add 1 and 2.

a=-232233

Rewrite 233 as 2.

Use axn=axn to rewrite 23 as 213.

a=-232(213)3

Apply the power rule and multiply exponents, (am)n=amn.

a=-232213⋅3

Combine 13 and 3.

a=-232233

Cancel the common factor of 3.

Cancel the common factor.

a=-232233

Divide 1 by 1.

a=-23221

a=-23221

Evaluate the exponent.

a=-2322

a=-2322

a=-2322

Simplify the numerator.

Rewrite 232 as (22)13.

a=-2232

Raise 2 to the power of 2.

a=-432

a=-432

a=-432

a=-432

a=-432

Substitute each value for a back into the function f(x)=ax to find each possible exponential function.

f(x)=(-432)x

Find the Exponential Function Given a Point (-3,-2)