Exponential function with negative base

[r0bHadz]

Homework Statement

-2^x = y

Homework Equations

The Attempt at a Solution

When I plug this function in my graphing calculator, it appears to be 2^x reflected across the x axis.

This doesn't make sense to me. For example, for x values of 1 and 2, the value of y is not on the same half of the graph.

Why is the graph then a reflection of 2^x?

 

[SammyS]

Homework Statement

-2^x = y

Homework Equations

The Attempt at a Solution

When I plug this function in my graphing calculator, it appears to be 2^x reflected across the x axis.

This doesn't make sense to me. For example, for x values of 1 and 2, the value of y is not on the same half of the graph.

Why is the graph then a reflection of 2^x?

If you really want the base to be negative you need it to be in parentheses.

(−2)^x

What you graphed was y = −(2^x)

 

[r0bHadz]

If you really want the base to be negative you need it to be in parentheses.

(−2)^x

What you graphed was y = −(2^x)

wooooww -_- i can't believe this right now. thanks mate lol.

 

[YoungPhysicist]

Just a quick note here, computing questions with negative base of any kind won’t work on a graphing calculator, for instance:
$$(-2)^x= 16$$
Though we all know the answer is x=4, it will throw an exception.

 

[Ray Vickson]

Just a quick note here, computing questions with negative base of any kind won’t work on a graphing calculator, for instance:
$$(-2)^x= 16$$
Though we all know the answer is x=4, it will throw an exception.

Right, and depending on exactly how powerful the calculator is, an entry like $(-2)^{3.5}$ will either give a "NO ANSWER" style of message, or else will output a complex number. Similarly, an equation like $(-2)^x = 3.5$ will choke a typical graphing calculator.