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, ∞)
