Answer to Question #154834 in Algebra for Zubin Chhaya

Question

Draw a graph of a function f(x)=x²+x

Answer 1

Step 1: Domain of x² + x : [solution: (- ∞ < x < ∞)] [Interval notion (-∞, ∞ )]

Domain definition

The domain of a function is a set of input or argument values for which the function is real and defined.

The function has no undefined points nor domain constraints. Therefore the domain is - ∞ < x < ∞

Step 2: Range x ² + x: [solution: f(x)≥ - 1/4] [Interval notion: (-1/4, ∞)]

Function range definition: the set of values of the dependent variables for which a function is defined.

Axis interception points of x² + x: x Intercepts (0,0), (-1,0), Y intercepts: (0,0)

Step 3: Vertex of x² + x: Minimum (-1/2, -1/4)

For parabola ax²+bx+c with vertex (x_v,y_v)

If a<0 the range f(x)≤yv

if a<0the range is f(x)≥y_v

a=1, Vertex (x_v,y_v) = (-1/2, -1/4)

f(x)≥-1/4

Therefore, Vertex of x² + x: Minimum (-1/2, -1/4)

The graph for the function f(x)=x²+x is provided in the image attached.