# Math

1.)Show and explain the stepsto Find the range of r(x) if given the function r(x)=5x+2/x-1

Find the range of h(x)=2x+1/x-3

1.)Given f(x)=6x^4-10x^3-4x^2

a)State the degree of the given function

b)Find all the zeros of the function and state its graph crosses or touches the x-axis at the zero.

c)Use the sign table to determine  the intervals where graph of y=f(x) lies above the x –axis and where f(x) lies below the x-axis.

d)Sketch the graph of f(x)

2)Given p(x)=x^3(2x+1)(x-1)^4

a)State the degree of the given function

b)Find the y-intercept of p(x)

c)Find all zeroes of the function

d)Give the multiplicity of all zeroes (x-intercepts) and state if the graph crosses or touches at the zeroes

e)State the intervals where the graph of p(x) lie above the x-axis

3.)Let f(x)= 1-x^2 if x< equal to 0

2x+1 if x >0

A)Evaluate f(-2) and f(1)

b)Sketch the graph

4.)Given -|x| if -2< than equal to 1

-x^2 if 1<x<2

if x> equal to 2

Find  a)g(1)b)g(5)

c)domain of g(x)

sketch the graph of g(x)

5.)Given f(x)= -1 if -2<x< equal to 1

Square root x (put x only under the square root)-1 if 1<x<4

3-x if x> equal to 4

Find:a) f(6)

b)f(-2)

c)f(1)

d)Domain of f(x)

What points to use to Sketch the graph of f(x)

5)state the transformations applied to the graph of f(x)=|x| to obtain the graph of g(x)=-2|x-3|+1

ii)Sketch the graph.Show and label at least 3 points of transformations used to draw your graph.

Consider the polynomial p(x)=2x^3+x^2-13x+6

a)Show using synthetic division that x=2 is a zero of p(x) (b)then factorize the quotient in a to find the other zeros of p(x)

c)Find the y intercept

f)Sketch the graph