Given:
The function is
[tex]f(x)=7x+11[/tex]
To find:
The domain, range, and intercepts of the function.
Solution:
We have,
[tex]f(x)=7x+11[/tex]
It is a linear function, and domain and range of these types of functions are all real numbers.
[tex]Domain:(-\infty,\infty)[/tex]
[tex]Range:(-\infty,\infty)[/tex]
Put x=0 in f(x), to find the y-intercept.
[tex]f(0)=7(0)+11[/tex]
[tex]f(0)=0+11[/tex]
[tex]f(0)=11[/tex]
So, the y-intercept is 11.
Put f(x)=0 in f(x), to find the x-intercept.
[tex]0=7x+11[/tex]
[tex]0-11=7x[/tex]
[tex]-11=7x[/tex]
Divide both sides by 7.
[tex]\dfrac{-11}{7}=x[/tex]
So, the x-intercept is [tex]\dfrac{-11}{7}[/tex].
Therefore, [tex]Domain:(-\infty,\infty), Range:(-\infty,\infty), x-intercept : (\dfrac{-11}{7},0),[/tex] [tex]y-intercept :11[/tex].
