Question

For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the following, and use it to graph the function.

Find: a)(2pts) Domain

b)(2pts) Intercepts

c)(2pts) Symmetry

d) (2pts) Asymptotes

e)(4pts) Intervals of Increase or decrease

f) (2pts) Local maximum and local minimum values

g)(4pts) Concavity and Points of inflection and

h)(2pts) Sketch the curve

Answer 1

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

is the set of real numbers.

Domain is i.e. all real numbers except " -3 and -1/2".

b) Intercepts:

• x-intercept: x-interept is a point on the graph where y=0

x-intercept is (0,0)

• y-intercept: y-intercept is a point on graph where x=0.

y-intercept is (0,0).

c) Symmetry

• Symmetry about y-axis: A graph is symmetric about y-axis if every 'x' on the graph can be replaced with '-x'

No symmetry about y-axis.

• Symmetry about x-axis: A graph is symmetric about the x-axis if every 'y' on the graph can be replaced with '-y'.

No symmetry about x-axis.

• Symmetry about origin: A graph is symmetric about the origin if every 'x' on the graph can be replaced with '-x' and every 'y' can be replaced with '-y'.

No symmetry about the origin.

d)Asymptotes

• Vertical asymptotes: For rational functions, the vertical asymptotes are the undefined points, also known as the zeroes of the denominator of the simplified function.

is the vertical asymptote.

• Horizontal asymptote:

If denominator's degree > numerator's degree , the horizontal asymptote is the x-axis : y=0

If numerator's degree = 1+ denominator's degree, the asymptote is a slant asymptote of the form : y=mx+b

If the degree are equal , the asymptote is : y=(numerator's leading coefficient) / (denominator's leading coefficient)

  is the horizontal asymptote.