Refer to the graph at the right. Find the value of f(7). Find the values of x co

Question

Refer to the graph at the right. Find the value of f(7). Find the values of x corresponding to the point(s) on the graph of f located at a height of 5 units from the x-axis. Find the point on the x-axis at which the graph of f crosses it. What is the value of f(x) at this point? Find the value(s) of x for which f(x) = -1. Find the domain of f. Find the range of f. Given f(x) = x + 1 and g(x) = x2 + 3. find g degree f and state its domain. Gift cards have increased in popularity in recent years. Consumers appreciate gift cards because they get to select the present they like. The U.S. sales of gift cards (in billions of dollars) is approximated by S(t) = -0.6204t3 + 4.671t3 + 3.354t + 47.4 in year t, where t = 0 corresponds to 2003. What were the sales of gift cards for 2003? What were the sales of gift cards for 2008? What are the projected sales of gift cards in 2014?

Explanation / Answer

(1)

from given figure

(a)

f(7)=3

(b)

the value of x where y=5

f(x)=5

and from figure

f(4)=5

therefore

x=4

(c)

at x=2, the graph crosses the x-axis.

at x=2,y=0

therefore

f(2)=0

(d)

f(x)=-1

grom the graph, we can see that the vaue of y=-1 is at x=-1 and at x=1 (approx)

so

f(-1)=-1 and

f(1)=-1

(e)

from the graph we can see that the value of x varies from x=-1 to x=9

so

domain of the function is [-1,9]

(f)

from the graph we can see that y can take value between y=-2 to y=6

so

range of the function is [-2,6]

(2)

f(x)=sqrt(x+1)

g(x)=x2+3

so

gof=g{f(x)}

g{x}=x2+3

g{f(x)}=g{sqrt(x+1)}={sqrt(x+1)}2+3

g{f(x)}=x+4

so

since it is a polinomial,

so it is defined all real number

so its domain is [-infinity,infinity]

(

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