Question

1-2 Attributes of Functions

Answer 1

Given:

The function is

$f(x)=7x+11$

To find:

The domain, range, and intercepts of the function.

Solution:

We have,

$f(x)=7x+11$

It is a linear function, and domain and range of these types of functions  are all real numbers.

$Domain:(-\infty,\infty)$

$Range:(-\infty,\infty)$

Put x=0 in f(x), to find the y-intercept.

$f(0)=7(0)+11$

$f(0)=0+11$

$f(0)=11$

So, the y-intercept is 11.

Put f(x)=0 in f(x), to find the x-intercept.

$0=7x+11$

$0-11=7x$

$-11=7x$

Divide both sides by 7.

$\dfrac{-11}{7}=x$

So, the x-intercept is $\dfrac{-11}{7}$.

Therefore, $Domain:(-\infty,\infty), Range:(-\infty,\infty), x-intercept : (\dfrac{-11}{7},0),$ $y-intercept :11$.