Graph f(x) = 2x +3

Question

Must graph the function and fill in the domain , range , vertex , maximum / minimum , increasing invertal , decreasing invertal , one to one and line of symmetry 

Answer 1

f(x) = 2x+3

 

Domain is all the valid values for x.

 

Any real number can be plugged in.

In interval notation, you can specify this as:  (-∞, ∞).

 

You also could say:  D = {all real numbers}

 

Range is all the y values or the possible values for f(x).

 

Since f(x) is the graph of a straight line, it will go forever in both the -y and +y directions.

 

R = (-∞, ∞) or {all real numbers}

 

Vertex:  straight line has no vertex.

 

f(x) has no maximum value.

f(x) has no minimum value.

 

 

The only way a line could have a minimum or maximum value would be if it had a slope of 0 (a horizontal line like y=5).

 

Since the slope or m = 2, the function is always increasing over the interval  (-∞, ∞).

 

It is 1-1 and there is no line of symmetry.

Answer 2

when a function approaches infinity we say there is no maximum rather than saying infinity is the maximum