Question

How would you do this type of problem and what would the increasing and decreasing interval be

Answer 1

y-intercept is the point in the y-axis that the graph intersects.

From the figure, the graph intersects at point (0, 3)

The y- intercept is (0, 3)

x-intercept is the point in the x-axis that the graph intersects.

Since the graph does not intersects the x-axis, the x-intercept does not exist

Vertex is a point on the graph that is a maximum or a minimum.

The vertex of the graph which is the lowest point as shown in the figure is at point (1, 2)

And this is a minima, since it is the lowest point.

Domain is the set of x-values that exist in the graph, the graph is going infinitely to the left and to the right, therefore the domain is (-∞, ∞)

Range is the set of y-values that exist in the graph, the y values starts from the vertex which is the lowest point at (1, 2) going upward.

So the range is all real numbers greater than or equal to 2. [2, ∞)

End behavior is the behavior of the function at large positive and negative values of x.

when x goes positive infinity, f(x) goes to positive infinity

As x ⇒ ∞, f(x) ⇒ ∞

when x goes negative infinity, f(x) goes to negative infinity

As x ⇒ -∞, f(x) ⇒ -∞

Decreasing interval occurs when the graph is going down, and increasing interval occurs when the graph is going up.

Decreasing interval will be (-∞, 1]

Increasing interval will be [1, ∞)