Question

determine whether each relation is a function. select \function\ or
ot a function\ for each graph.

graph 1:
a curve plotted on a cartesian coordinate plane. the curve opens to the right, starting near (x = -1, y = 1), passing through ((1, 0)), ((3, -1)), and continuing downwards and to the left, as well as upwards and to the right.

graph 2:
an ellipse plotted on a cartesian coordinate plane. the ellipse is centered at ((1, -2)) with a horizontal major axis of length 4 (from (x = -1) to (x = 3)) and a vertical minor axis of length 2 (from (y = -1) to (y = -3)).

Explanation:

Step1: Identify the curve type

The graph shows a cubic curve oriented horizontally.

Step2: Locate the inflection point

The inflection point of the curve is at \((2, -1)\).

Step3: Determine the equation form

A horizontal cubic curve has the standard form:

$$(y - k)^3 = a(x - h)$$

Step4: Substitute the inflection point

Substitute \((h, k) = (2, -1)\) into the equation:

$$(y + 1)^3 = a(x - 2)$$

Step5: Find the scaling factor

Using the point \((3, 0)\) on the graph:

$$(0 + 1)^3 = a(3 - 2) \implies 1 = a$$

Step6: Write the final equation

Substitute \(a = 1\) back into the equation:

$$(y + 1)^3 = x - 2$$

Answer:

The equation of the graphed relation is:

$$(y + 1)^3 = x - 2$$