Answer:
a) Function:Yes
b) Domain: [tex]-5\:<\:x\:<\:4[/tex]
c) Range: [tex]-5\le y\le 3[/tex]
Step-by-step explanation:
The given graph passes vertical line test hence it is a function
The given function has x-intercepts at [tex]x=-4.5, x=-1,x=3.5[/tex]
We can therefore write this function in factored form as [tex]y=a(2x+9)(x+1)(2x-7)[/tex]
There is a y-intercept at (0,-2)
[tex]-2=a(2*0+9)(0+1)(2*0-7)[/tex]
[tex]-2=-63a[/tex]
[tex]a=\frac{2}{63}[/tex]
The required function is
[tex]y=\frac{2}{63}(2x+9)(x+1)(2x-7)[/tex]
b) The domain refers to all values of x for which this function is defined.
The domain from the graph is [tex]-5\:<\:x\:<\:4[/tex] because there are holes at the end of the graph.
c) The range is the value of y for which x is defined or the graph exists.
From the graph the range is [tex]-5\le y\le 3[/tex]
