Question

Does the graph of the function contain the point \((0,1) ?\) $$y=4 \cdot 1^{x}$$

Short answer

No, the point (0,1) does not lie on the graph of the function \(y=4 \cdot 1^{x}\).

Step-by-step solution

Substitute the x-coordinate

Substitute the x-coordinate of the point into the function. The given x-coordinate is 0, so \(y=4 \cdot 1^{0}\).

Simplify the expression

Since any real number raised to the power of 0 is 1, the expression simplifies to \(y=4 \cdot 1=4\).

Compare the y-coordinate

Compare the resulting y-coordinate with the y-coordinate of the given point. If they match, the point lies on the graph. Here, the resulting y-coordinate is 4, while the y-coordinate of the point given is 1. They do not match.