Question

Given the following linear function sketch the graph of the function and find the domain and range.

ƒ(x) = -5x + 4

Answer 1

Domain of the given function is all real numbers and the range of the function all real numbers.

Explanation:

The given function is

`f(x)=-5x+4` .... (1)

The slope intercept form of a line function is

`y=mx+b` .... (2)

Where, m is slope and b is y-intercept.

From (1) and (2), we get

`m=-5,b=4`

It means the slope of the line is -5 and y-intercept is 4.

Draw a line with slope -5 and y-intercept 4 on a coordinate plane as show below.

Domain is the set of inputs and range is the set of outputs.

The function is defined for all values of x. So, the domain of the function is all real numbers.

`Domain=\x`

The value of function can be any real number. So, the range of the function is all real numbers.

`Range=\y`

Therefore, the domain of the given function is all real numbers and the range of the function all real numbers.