Question

1. use these key features to sketch the graph of f(x):

• non - linear
• y - intercept located at (0,2)
• relative min at (-2,-4) and an absolute min at (2,-6)
• end behavior: as x→ - ∞, y→∞ as x→∞, y→∞

Explanation:

Step1: Plot y - intercept

Plot the point $(0,2)$ on the coordinate - plane. This is where the graph crosses the y - axis.

Step2: Plot relative minimum

Plot the point $(-2, - 4)$. This is a local low - point of the function.

Step3: Plot absolute minimum

Plot the point $(2,-6)$. This is the overall low - point of the function.

Step4: Consider end - behavior

As $x\to-\infty,y\to\infty$ and as $x\to\infty,y\to\infty$. So, the graph starts from the upper left and goes to the upper right. Then, connect the points in a smooth non - linear curve.

Answer:

Sketch a non - linear curve that passes through the points $(0,2),(-2, - 4),(2,-6)$ and has the appropriate end - behavior (rises to the left and rises to the right).