Question

The function f is defined as follows for the domain given. f(x)= 2x+2 domain = (-4, -1, 1, 3)Write the range of f using set notation. Then graph f.

Answer 1

Given that,

The function f is defined as

`f\mleft(x\mright)=2x+2`

domain = (-4, -1, 1, 3)

To find the range of f using set notation and graph f

When x=-4,

Substitute in f(x), we get,

`f\mleft(-4\mright)=2\left(-4\right)+2`
`=-8+2=-6----\left(1\right)`

When x=-1

Substitute in f(x), we get

`f\mleft(-1\mright)=2\left(-1\right)+2`
`=-2+2=0-------\left(2\right)`

When x=1

Substitute in f(x), we get

`f\mleft(1\mright)=2\left(1\right)+2`
`=4------\left(3\right)`

when x=3

Substitute in f(x), we get

`f\mleft(3\mright)=2\left(3\right)+2`
`=6+2=8-------\left(4\right)`

From (1), (2), (3), (4), we get the,

Range of f as {-6,0,4,8}

Then the graph of f is given by,

Slope is 2 and y intercept is 2.

Plotting the given points we get,