Exam 3: Functions and Graphs

Determine whether the graph of = 4 is symmetric about the x-axis,the y-axis,the origin,or the line y = x.

The elapsed time in seconds since January 1,2000 at 12:00 a.m.depends on the elapsed hours since January 1,2000 at 12:00 a.m. (a)Write a function e(h)for the elapsed seconds since January 1,2000 at 12:00 a.m.when the elapsed hours are h. (b)What is the domain of the function out of context? (c)What is the domain of this function in the given context? (d)Find e(t),e(-t),e(100t),and e(-100t). (e)What does multiplying the elapsed hour by -1 mean?

By looking a the graph below: (a)list all values for which f(x)= -2 (b)f(-1)= (c)f(0)= (d)domain of f(x)is? (e)range of f(x)is?

A cylinder has a height that is 3 times as long as the radius. (a)Write the area of its circular base as a function of its radius. (b)Write the volume of the cylinder as a function of its radius. (c)Without simplifying,write the ratio of the area of the circular base and the volume of the cylinder as a function of the radius. (d)Simplify the function you wrote in c. (e)What kind of function is this? (f)What is its domain out of context? (g)What is its domain in the given context?

Determine the x- and y-intercepts of the graph of y = - 4x.

The height of an object thrown in the air depends on the time since it has been thrown.For a particular situation the height in meters of an object after t seconds can be represented by h(t)= 32t - 4.9 . (a)What kind of function is this? (b)What is its degree? (c)What is its leading coefficient?

The perimeter of a square depends on the length of its side. (a)Write a function p(l)for the perimeter of a square. (b)How much linear fencing material is needed to fence a square garden of length x? (c)If the sides of the square garden are increased by 3 feet,how much more linear fencing material is needed? (d)How much more linear fencing material is needed per foot increase? (e)If the sides of the square garden is increased by h,how much more linear fencing material is needed? (f)How much more linear fencing material is needed per unit increase?

Sketch the surface 3x + y + 2z = 6.

If f(x)= ,then find and simplify.

Determine the x- and y-intercepts of the graph of + = 1.

Determine whether or not the function is one-to-one: f(x)= - 8.

An equation of the plane that is parallel to the x,y-plane and that passes through (2,7,3)is

For the equation 4y = ,(a)is y a function of x? (b)Is x a function of y?

(a)Sketch the graph of y = 2x + 1.(b)Determine the intercepts. (c)Based on your graph,is y a function of x? If so,state (d)the domain and (e)the range.

Let g(x)= 1 - 4x,h(x)= + 3x.Find: (a)(g ∘ h)(x); (b)(h∘ g)(x)

The graph of y = f(x)is shown below.Estimate: (a)f(-1) (b)f(0) (c)f(2) (d)f(3) (e)What is the domain of f? (f)What is the range of f?

Suppose the volume of a cube is v(x)= (x - .Express as a composition of two functions and explain what each function represents.

If g(x)= ,find: (a)the domain (b)g(0) (c)g(-4) (d)g (e)g( )

If F(t)= ( + ,then F( + 1)=

h(x)= - 7 + 1; g(x)= + 2x.Find (a)(h + g)(.1) (b)(h - g)(.1) (c)(hg)(.1) (d) (.1)