Question

(a) Graph the function $f\left(x\right)=3x+4$.

(b)state its domain and range. Write the domain and range in interval notation.

Short answer

The graph of f(x) is

$$\begin{gathered} domain:(-\infty ,\infty ) \\ Range:(-\infty ,\infty ) \end{gathered}$$

Step-by-step solution

Given Information 

Given function is

$f\left(x\right)=3x+4$

Part(a) Step 1:  Graph the function 

The given function f(x) is in the form of $f\left(x\right)=mx+b$

where m is the slope and b is the y intercept .

$f\left(x\right)=3x+4$

slope =3

y intercept=4

Plot the y intercept (0,4). Now use the slope =3

Move 3 units up and 1 unit to the right .

Plot the point at (1,7). Connect the points by a line .

The graph of the function is

Part (b) Step 1: Domain and Range

Domain is the set of x values for which the function is defined.

The graph is defined for all x values .

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

Range is the set of y values for which the function is defined. The graph is defined for all y values.

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