Question

Attempted but just couldnt understand (25Points)​

Answer 1

a) Function:Yes

b) Domain:
`-5\:<\:x\:<\:4`

c) Range:
`-5\le y\le 3`

Explanation:

The given graph passes vertical line test hence it is a function

The given function has x-intercepts at
`x=-4.5, x=-1,x=3.5`

We can therefore write this function in factored form as
`y=a(2x+9)(x+1)(2x-7)`

There is a y-intercept at (0,-2)

`-2=a(2*0+9)(0+1)(2*0-7)`

`-2=-63a`

`a=(2)/(63)`

The required function is

`y=(2)/(63)(2x+9)(x+1)(2x-7)`

b) The domain refers to all values of x for which this function is defined.

The domain from the graph is
`-5\:<\:x\:<\:4` 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
`-5\le y\le 3`