The graph of a quadratic function with vertex (4, 1) is shown in the figure below. Find the domain and the range.

Domain: All reals

Range: y < 1 OR 1 > y

Step-by-step explanation:

Domain is all the x values the line passes through.

Range is all the y values the line passes through.

Every parabola has a domain of all real numbers since they all stretch out to infinity on the x axis.

This parabola stops going up at y = 1, so the range is all real numbers below 1, which is either y < 1 or 1 > y.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.