Question

Does the graph of the function contain the point \((0,1) ?\) $$y=-3^{x}$$

Short answer

No, the point \((0,1)\) does not lie on the graph of the function \(y=-3^{x}\).

Step-by-step solution

Understand the function

The function in question is \(y=-3^{x}\). This function returns the negative of three raised to the power of x.

Substitute the point into the function

The x and y coordinates of the point are 0 and 1, respectively. Therefore, by substituting these values into the function,y becomes 1 and x becomes 0. So, after substitution, the equation becomes 1 = -3^{0}.

Evaluate the equation

The expression -3^{0} equals -1 because any number (except zero) to the power of 0 is 1, but since it's -3^{0} the result will be -1.

Compare the results

After evaluating, the result is -1. But y coordinate of given point is 1. Hence, the point \((0,1)\) does not satisfy the function.